Systems and methods for navigating a vehicle

ABSTRACT

Systems and methods are provided for vehicle navigation. In one implementation, a system may comprise an interface to obtain sensing data of an environment of the host vehicle. A processing device may be configured to determine a planned navigational action for the host vehicle; identify a target vehicle in the environment of the host vehicle; predict a following distance between the host vehicle and the target vehicle that would result if the planned navigational action was taken; determine a host vehicle braking distance based on a braking capability, acceleration capability, and speed of the host vehicle; determine a target vehicle braking distance, based on a speed and maximum braking capability of the target vehicle; and implement the planned navigational action when the predicted following distance is greater than a minimum safe longitudinal distance based on the determined host vehicle braking distance and the determined target vehicle braking distance.

CROSS REFERENCES TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/359,488, filed Mar. 20, 2019, which claims the benefit of priority ofU.S. Provisional Patent Application No. 62/645,479, filed on Mar. 20,2018; U.S. Provisional Patent Application No. 62/646,579, filed on Mar.22, 2018; U.S. Provisional Patent Application No. 62/718,554, filed onAug. 14, 2018; U.S. Provisional Patent Application No. 62/724,355, filedon Aug. 29, 2018; U.S. Provisional Patent Application No. 62/772,366,filed on Nov. 28, 2018; and U.S. Provisional Patent Application No.62/777,914, filed on Dec. 11, 2018. All of the foregoing applicationsare incorporated herein by reference in their entirety.

BACKGROUND Technical Field

The present disclosure relates generally to autonomous vehiclenavigation. Additionally, this disclosure relates to systems and methodsfor navigating according to potential accident liability constraints.

Background Information

As technology continues to advance, the goal of a fully autonomousvehicle that is capable of navigating on roadways is on the horizon.Autonomous vehicles may need to take into account a variety of factorsand make appropriate decisions based on those factors to safely andaccurately reach an intended destination. For example, an autonomousvehicle may need to process and interpret visual information (e.g.,information captured from a camera), information from radar or lidar,and may also use information obtained from other sources (e.g., from aGPS device, a speed sensor, an accelerometer, a suspension sensor,etc.). At the same time, in order to navigate to a destination, anautonomous vehicle may also need to identify its location within aparticular roadway (e.g., a specific lane within a multi-lane road),navigate alongside other vehicles, avoid obstacles and pedestrians,observe traffic signals and signs, travel from one road to another roadat appropriate intersections or interchanges, and respond to any othersituation that occurs or develops during the vehicle's operation.Moreover, the navigational system may need to adhere to certain imposedconstraints. In some cases, those constraints may relate to interactionsbetween a host vehicle and one or more other objects, such as othervehicles, pedestrians, etc. In other cases, the constraints may relateto liability rules to be followed in implementing one or morenavigational actions for a host vehicle.

In the field of autonomous driving, there are two importantconsiderations for viable autonomous vehicle systems. The first is astandardization of safety assurance, including requirements that everyself-driving car must satisfy to ensure safety, and how thoserequirements can be verified. The second is scalability, as engineeringsolutions that lead to unleashed costs will not scale to millions ofcars and may prevent widespread or even not so widespread adoption ofautonomous vehicles. Thus, there is a need for an interpretable,mathematical model for safety assurance and a design of a system thatadheres to safety assurance requirements while being scalable tomillions of cars.

SUMMARY

Embodiments consistent with the present disclosure provide systems andmethods for autonomous vehicle navigation. The disclosed embodiments mayuse cameras to provide autonomous vehicle navigation features. Forexample, consistent with the disclosed embodiments, the disclosedsystems may include one, two, or more cameras that monitor theenvironment of a vehicle. The disclosed systems may provide anavigational response based on, for example, an analysis of imagescaptured by one or more of the cameras. The navigational response mayalso take into account other data including, for example, globalpositioning system (GPS) data, sensor data (e.g., from an accelerometer,a speed sensor, a suspension sensor, etc.), and/or other map data.

In an embodiment, a system for navigating a host vehicle may include atleast one processing device programmed to receive at least one imagerepresentative of an environment of the host vehicle. The at least oneimage may be received from an image capture device. The at least oneprocessing device may be programmed to determine, based on at least onedriving policy, a planned navigational action for accomplishing anavigational goal of the host vehicle. The at least one processingdevice may be further programmed to analyze the at least one image toidentify a target vehicle in the environment of the host vehicle and todetermine a next-state distance between the host vehicle and the targetvehicle that would result if the planned navigational action was taken.The at least one processing device may be programmed to determine amaximum braking capability of the host vehicle, a maximum accelerationcapability of the host vehicle, and a current speed of the host vehicle.The at least one processing device may also be programmed to determine acurrent stopping distance for the host vehicle based on the currentmaximum braking capability of the host vehicle, the current maximumacceleration capability of the host vehicle, and the current speed ofthe host vehicle. The at least one processing device may be furtherprogrammed to determine a current speed of the target vehicle and toassume a maximum braking capability of the target vehicle based on atleast one recognized characteristic of the target vehicle. The at leastone processing device may also be programmed to implement the plannednavigational action if the determined current stopping distance for thehost vehicle is less than the determined next-state distance summedtogether with a target vehicle travel distance determined based on thecurrent speed of the target vehicle and the assumed maximum brakingcapability of the target vehicle.

In an embodiment, a system for navigating a host vehicle may include atleast one processing device. The at least one processing device may beprogrammed to receive, from an image capture device, at least one imagerepresentative of an environment of the host vehicle. The at least oneprocessing device may also be programmed to determine a plannednavigational action for accomplishing a navigational goal of the hostvehicle. The planned navigational action may be based on at least onedriving policy. The at least one processing device may be programmed toanalyze the at least one image to identify a target vehicle in theenvironment of the host vehicle. The at least one processing device maybe further programmed to determine a next-state distance between thehost vehicle and the target vehicle that would result if the plannednavigational action was taken. The at least one processing device may beprogrammed to determine a current speed of the host vehicle and acurrent speed of the target vehicle. The at least one processing deicemay be programmed to assume a maximum braking rate capability of thetarget vehicle based on at least one recognized characteristic of thetarget vehicle. The at least one processing device may be furtherconfigured to implement the planned navigational action if, for thedetermined current speed of the host vehicle and at a predeterminedsub-maximal braking rate that is less than a maximum braking ratecapability of the host vehicle, the host vehicle can be stopped within ahost vehicle stopping distance that is less than the determinednext-state distance summed together with a target vehicle traveldistance determined based on the current speed of the target vehicle andthe assumed maximum braking rate capability of the target vehicle.

In an embodiment, a system for navigating a host vehicle may include atleast one processing device. The at least one processing device may beprogrammed to receive, from an image capture device, at least one imagerepresentative of an environment of the host vehicle. The at least oneprocessing device may also be programmed to determine a plannednavigational action for accomplishing a navigational goal of the hostvehicle. The planned navigational action may be based on at least onedriving policy. The at least one processing device may be programmed toanalyze the at least one image to identify a target vehicle in theenvironment of the host vehicle. The at least one processing device maybe further programmed to determine a next-state distance between thehost vehicle and the target vehicle that would result if the plannednavigational action was taken. The at least one processing device may beprogrammed to determine a current speed of the host vehicle. The atleast one processing deice may be programmed to determine a currentspeed of the target vehicle and to assume a maximum braking ratecapability of the target vehicle based on at least one recognizedcharacteristic of the target vehicle. The at least one processing devicemay be programmed to implement the planned navigational action if, forthe determined current speed of the host vehicle and for a predeterminedbraking rate profile, the host vehicle can be stopped within a hostvehicle stopping distance that is less than the determined next-statedistance summed together with a target vehicle travel distancedetermined based on the current speed of the target vehicle and theassumed maximum braking rate capability of the target vehicle, whereinthe predetermined braking rate profile progressively increases from asub-maximal braking rate to a maximal braking rate for the host vehicle.

In an embodiment, a system for braking a host vehicle may include atleast one processing device programmed to perform one or moreoperations. The at least one processing device may be programmed toreceive, from at least one sensor, an output representative of anenvironment of the host vehicle. The at least one processing device mayfurther be programmed to detect, based on the output, a target vehiclein the environment of the host vehicle. The at least one processingdevice may be programmed to determine a current speed of the hostvehicle and a current distance between the host vehicle and the targetvehicle. Based on at least upon the current speed of the host vehicleand the current distance between the host vehicle and the targetvehicle, the at least one processor may be programmed to determinewhether a braking condition exists. If a braking condition is determinedto exist, the at least one processor may be programmed to causeapplication of a braking device associated with the host vehicleaccording to a predetermined braking profile including a segmentbeginning at a sub-maximal braking rate for the host vehicle andprogressively increasing up to a maximum braking rate of the hostvehicle.

In an embodiment, an autonomous system for selectively displacing humandriver control of a host vehicle may include at least one processingdevice. The at least one processing device may be programmed to receive,from an image capture device, at least one image representative of anenvironment of the host vehicle and to detect at least one obstacle inthe environment of the host vehicle based on analysis of the at leastone image. The at least one processing device may be programmed tomonitor a driver input to at least one of a throttle control, a brakecontrol, or a steering control associated with the host vehicle. The atleast one processing device may also be programmed to determine whetherthe driver input would result in the host vehicle navigating within aproximity buffer relative to the at least one obstacle. If the at leastone processing device determines that the driver input would not resultin the host vehicle navigating within the proximity buffer relative tothe at least one obstacle, the at least one processing device may beprogrammed to allow the driver input to cause a corresponding change inone or more host vehicle motion control systems. If the at least oneprocessing device determines that the driver input would result in thehost vehicle navigating within the proximity buffer relative to the atleast one obstacle, the at least one processing device may be programmedto prevent the driver input from causing the corresponding change in theone or more host vehicle motion control systems.

In an embodiment, a navigation system for navigating an autonomous hostvehicle according to at least one navigational goal of the host vehiclemay include at least one processor. The at least one processor may beprogrammed to receive, from one or more sensors, a sensor outputindicative of at least one aspect of motion of the host vehicle relativeto an environment of the host vehicle. The sensor output may begenerated at a first time that is later than a data acquisition time,when a measurement or data acquisition on which the sensor output isbased is acquired, and earlier than a second time at which the sensoroutput is received by the at least one processor. The at least oneprocessor may be programmed to generate, for a motion prediction time, aprediction of at least one aspect of host vehicle motion based, at leastin part, on the received sensor output and an estimation of how the atleast one aspect of host vehicle motion changes over a time intervalbetween the data acquisition time and the motion prediction time. The atleast one processor may be programmed to determine a plannednavigational action for the host vehicle based, at least in part, on theat least one navigational goal of the host vehicle and based on thegenerated prediction of the at least one aspect of host vehicle motion.The at least one processor may be further configured to generate anavigational command for implementing at least a portion of the plannednavigational action. The at least one processor may be programmed toprovide the navigational command to at least one actuation system of thehost vehicle. The navigational command may be provided such that the atleast one actuation system receives the navigational command at a thirdtime that is later than the second time and earlier or substantially thesame as an actuation time at which a component of the at least oneactuation system responds to the received command. In some embodiments,the motion prediction time is after the data acquisition time andearlier than or equal to the actuation time.

Consistent with other disclosed embodiments, non-transitorycomputer-readable storage media may store program instructions, whichare executable by at least one processing device and perform any of thesteps and/or methods described herein.

The foregoing general description and the following detailed descriptionare exemplary and explanatory only and are not restrictive of theclaims.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this disclosure, illustrate various disclosed embodiments. Inthe drawings:

FIG. 1 is a diagrammatic representation of an exemplary systemconsistent with the disclosed embodiments.

FIG. 2A is a diagrammatic side view representation of an exemplaryvehicle including a system consistent with the disclosed embodiments.

FIG. 2B is a diagrammatic top view representation of the vehicle andsystem shown in FIG. 2A consistent with the disclosed embodiments.

FIG. 2C is a diagrammatic top view representation of another embodimentof a vehicle including a system consistent with the disclosedembodiments.

FIG. 2D is a diagrammatic top view representation of yet anotherembodiment of a vehicle including a system consistent with the disclosedembodiments.

FIG. 2E is a diagrammatic top view representation of yet anotherembodiment of a vehicle including a system consistent with the disclosedembodiments.

FIG. 2F is a diagrammatic representation of exemplary vehicle controlsystems consistent with the disclosed embodiments.

FIG. 3A is a diagrammatic representation of an interior of a vehicleincluding a rearview mirror and a user interface for a vehicle imagingsystem consistent with the disclosed embodiments.

FIG. 3B is an illustration of an example of a camera mount that isconfigured to be positioned behind a rearview mirror and against avehicle windshield consistent with the disclosed embodiments.

FIG. 3C is an illustration of the camera mount shown in FIG. 3B from adifferent perspective consistent with the disclosed embodiments.

FIG. 3D is an illustration of an example of a camera mount that isconfigured to be positioned behind a rearview mirror and against avehicle windshield consistent with the disclosed embodiments.

FIG. 4 is an exemplary block diagram of a memory configured to storeinstructions for performing one or more operations consistent with thedisclosed embodiments.

FIG. 5A is a flowchart showing an exemplary process for causing one ormore navigational responses based on monocular image analysis consistentwith disclosed embodiments.

FIG. 5B is a flowchart showing an exemplary process for detecting one ormore vehicles and/or pedestrians in a set of images consistent with thedisclosed embodiments.

FIG. 5C is a flowchart showing an exemplary process for detecting roadmarks and/or lane geometry information in a set of images consistentwith the disclosed embodiments.

FIG. 5D is a flowchart showing an exemplary process for detectingtraffic lights in a set of images consistent with the disclosedembodiments.

FIG. 5E is a flowchart showing an exemplary process for causing one ormore navigational responses based on a vehicle path consistent with thedisclosed embodiments.

FIG. 5F is a flowchart showing an exemplary process for determiningwhether a leading vehicle is changing lanes consistent with thedisclosed embodiments.

FIG. 6 is a flowchart showing an exemplary process for causing one ormore navigational responses based on stereo image analysis consistentwith the disclosed embodiments.

FIG. 7 is a flowchart showing an exemplary process for causing one ormore navigational responses based on an analysis of three sets of imagesconsistent with the disclosed embodiments.

FIG. 8 is a block diagram representation of modules that may beimplemented by one or more specifically programmed processing devices ofa navigation system for an autonomous vehicle consistent with thedisclosed embodiments.

FIG. 9 is a navigation options graph consistent with the disclosedembodiments.

FIG. 10 is a navigation options graph consistent with the disclosedembodiments.

FIGS. 11A, 11B, and 11C provide a schematic representation ofnavigational options of a host vehicle in a merge zone consistent withthe disclosed embodiments.

FIG. 11D provide a diagrammatic depiction of a double merge scenarioconsistent with the disclosed embodiments.

FIG. 11E provides an options graph potentially useful in a double mergescenario consistent with the disclosed embodiments.

FIG. 12 provides a diagram of a representative image captured of anenvironment of a host vehicle, along with potential navigationalconstraints consistent with the disclosed embodiments.

FIG. 13 provides an algorithmic flow chart for navigating a vehicleconsistent with the disclosed embodiments.

FIG. 14 provides an algorithmic flow chart for navigating a vehicleconsistent with the disclosed embodiments.

FIG. 15 provides an algorithmic flow chart for navigating a vehicleconsistent with the disclosed embodiments.

FIG. 16 provides an algorithmic flow chart for navigating a vehicleconsistent with the disclosed embodiments.

FIGS. 17A and 17B provide a diagrammatic illustration of a host vehiclenavigating into a roundabout consistent with the disclosed embodiments.

FIG. 18 provides an algorithmic flow chart for navigating a vehicleconsistent with the disclosed embodiments.

FIG. 19 illustrates an example of a host vehicle driving on a multi-lanehighway consistent with the disclosed embodiments.

FIGS. 20A and 20B illustrate examples of a vehicle cutting in in frontof another vehicle consistent with the disclosed embodiments.

FIG. 21 illustrates an example of a vehicle following another vehicleconsistent with the disclosed embodiments.

FIG. 22 illustrates an example of a vehicle exiting a parking lot andmerging into a possibly busy road consistent with the disclosedembodiments.

FIG. 23 illustrates a vehicle traveling on a road consistent with thedisclosed embodiments.

FIGS. 24A-24D illustrate four example scenarios consistent with thedisclosed embodiments.

FIG. 25 illustrates an example scenario consistent with the disclosedembodiments.

FIG. 26 illustrates an example scenario consistent with the disclosedembodiments.

FIG. 27 illustrates an example scenario consistent with the disclosedembodiments.

FIGS. 28A and 28B illustrate an example of a scenario in which a vehicleis following another vehicle consistent with the disclosed embodiments.

FIGS. 29A and 29B illustrate example blame in cut-in scenariosconsistent with the disclosed embodiments.

FIGS. 30A and 30B illustrate example blame in cut-in scenariosconsistent with the disclosed embodiments.

FIGS. 31A-31D illustrate example blame in drifting scenarios consistentwith the disclosed embodiments.

FIGS. 32A and 32B illustrate example blame in two-way traffic scenariosconsistent with the disclosed embodiments.

FIGS. 33A and 33B illustrate example blame in two-way traffic scenariosconsistent with the disclosed embodiments.

FIGS. 34A and 34B illustrate example blame in route priority scenariosconsistent with the disclosed embodiments.

FIGS. 35A and 35B illustrate example blame in route priority scenariosconsistent with the disclosed embodiments.

FIGS. 36A and 36B illustrate example blame in route priority scenariosconsistent with the disclosed embodiments.

FIGS. 37A and 37B illustrate example blame in route priority scenariosconsistent with the disclosed embodiments.

FIGS. 38A and 38B illustrate example blame in route priority scenariosconsistent with the disclosed embodiments.

FIGS. 39A and 39B illustrate example blame in route priority scenariosconsistent with the disclosed embodiments.

FIGS. 40A and 40B illustrate example blame in traffic light scenariosconsistent with the disclosed embodiments.

FIGS. 41A and 41B illustrate example blame in traffic light scenariosconsistent with the disclosed embodiments.

FIGS. 42A and 42B illustrate example blame in traffic light scenariosconsistent with the disclosed embodiments.

FIGS. 43A-43C illustrate example vulnerable road users (VRUs) scenariosconsistent with the disclosed embodiments.

FIGS. 44A-44C illustrate example vulnerable road users (VRUs) scenariosconsistent with the disclosed embodiments.

FIGS. 45A-45C illustrate example vulnerable road users (VRUs) scenariosconsistent with the disclosed embodiments.

FIGS. 46A-46D illustrate example vulnerable road users (VRUs) scenariosconsistent with the disclosed embodiments.

FIGS. 47A and 47B illustrate example scenarios in which a vehicle isfollowing another vehicle consistent with the disclosed embodiments.

FIG. 48 is a flowchart showing an exemplary process for navigating ahost vehicle consistent with the disclosed embodiments.

FIGS. 49A-49D illustrate example scenarios in which a vehicle isfollowing another vehicle consistent with the disclosed embodiments.

FIG. 50 is a flowchart showing an exemplary process for braking a hostvehicle consistent with the disclosed embodiments.

FIG. 51 is a flowchart showing an exemplary process for navigating ahost vehicle consistent with the disclosed embodiments.

FIGS. 52A-52D illustrate example proximity buffers for a host vehicleconsistent with the disclosed embodiments.

FIGS. 53A and 53B illustrate example scenarios including a proximitybuffer consistent with the disclosed embodiments.

FIGS. 54A and 54B illustrate example scenarios including a proximitybuffer consistent with the disclosed embodiments.

FIG. 55 provides a flowchart for selectively displacing a human drivercontrol of a host vehicle consistent with the disclosed embodiments.

FIG. 56 is a flowchart showing an exemplary process for navigating ahost vehicle consistent with the disclosed embodiments.

FIGS. 57A-57C illustrate example scenarios consistent with the disclosedembodiments.

FIG. 58 is a flowchart showing an exemplary process for navigating ahost vehicle consistent with the disclosed embodiments.

DETAILED DESCRIPTION

The following detailed description refers to the accompanying drawings.Wherever possible, the same reference numbers are used in the drawingsand the following description to refer to the same or similar parts.While several illustrative embodiments are described herein,modifications, adaptations and other implementations are possible. Forexample, substitutions, additions or modifications may be made to thecomponents illustrated in the drawings, and the illustrative methodsdescribed herein may be modified by substituting, reordering, removing,or adding steps to the disclosed methods. Accordingly, the followingdetailed description is not limited to the disclosed embodiments andexamples. Instead, the proper scope is defined by the appended claims.

Autonomous Vehicle Overview

As used throughout this disclosure, the term “autonomous vehicle” refersto a vehicle capable of implementing at least one navigational changewithout driver input. A “navigational change” refers to a change in oneor more of steering, braking, or acceleration/deceleration of thevehicle. To be autonomous, a vehicle need not be fully automatic (e.g.,fully operational without a driver or without driver input). Rather, anautonomous vehicle includes those that can operate under driver controlduring certain time periods and without driver control during other timeperiods. Autonomous vehicles may also include vehicles that control onlysome aspects of vehicle navigation, such as steering (e.g., to maintaina vehicle course between vehicle lane constraints) or some steeringoperations under certain circumstances (but not under allcircumstances), but may leave other aspects to the driver (e.g., brakingor braking under certain circumstances). In some cases, autonomousvehicles may handle some or all aspects of braking, speed control,and/or steering of the vehicle.

As human drivers typically rely on visual cues and observations in orderto control a vehicle, transportation infrastructures are builtaccordingly, with lane markings, traffic signs, and traffic lightsdesigned to provide visual information to drivers. In view of thesedesign characteristics of transportation infrastructures, an autonomousvehicle may include a camera and a processing unit that analyzes visualinformation captured from the environment of the vehicle. The visualinformation may include, for example, images representing components ofthe transportation infrastructure (e.g., lane markings, traffic signs,traffic lights, etc.) that are observable by drivers and other obstacles(e.g., other vehicles, pedestrians, debris, etc.). Additionally, anautonomous vehicle may also use stored information, such as informationthat provides a model of the vehicle's environment when navigating. Forexample, the vehicle may use GPS data, sensor data (e.g., from anaccelerometer, a speed sensor, a suspension sensor, etc.), and/or othermap data to provide information related to its environment while it istraveling, and the vehicle (as well as other vehicles) may use theinformation to localize itself on the model. Some vehicles can also becapable of communication among them, sharing information, altering thepeer vehicle of hazards or changes in the vehicles' surroundings, etc.

System Overview

FIG. 1 is a block diagram representation of a system 100 consistent withthe exemplary disclosed embodiments. System 100 may include variouscomponents depending on the requirements of a particular implementation.In some embodiments, system 100 may include a processing unit 110, animage acquisition unit 120, a position sensor 130, one or more memoryunits 140, 150, a map database 160, a user interface 170, and a wirelesstransceiver 172. Processing unit 110 may include one or more processingdevices. In some embodiments, processing unit 110 may include anapplications processor 180, an image processor 190, or any othersuitable processing device. Similarly, image acquisition unit 120 mayinclude any number of image acquisition devices and components dependingon the requirements of a particular application. In some embodiments,image acquisition unit 120 may include one or more image capture devices(e.g., cameras, CCDs, or any other type of image sensor), such as imagecapture device 122, image capture device 124, and image capture device126. System 100 may also include a data interface 128 communicativelyconnecting processing unit 110 to image acquisition unit 120. Forexample, data interface 128 may include any wired and/or wireless linkor links for transmitting image data acquired by image acquisition unit120 to processing unit 110.

Wireless transceiver 172 may include one or more devices configured toexchange transmissions over an air interface to one or more networks(e.g., cellular, the Internet, etc.) by use of a radio frequency,infrared frequency, magnetic field, or an electric field. Wirelesstransceiver 172 may use any known standard to transmit and/or receivedata (e.g., Wi-Fi, Bluetooth®, Bluetooth Smart, 802.15.4, ZigBee, etc.).Such transmissions can include communications from the host vehicle toone or more remotely located servers. Such transmissions may alsoinclude communications (one-way or two-way) between the host vehicle andone or more target vehicles in an environment of the host vehicle (e.g.,to facilitate coordination of navigation of the host vehicle in view ofor together with target vehicles in the environment of the hostvehicle), or even a broadcast transmission to unspecified recipients ina vicinity of the transmitting vehicle.

Both applications processor 180 and image processor 190 may includevarious types of hardware-based processing devices. For example, eitheror both of applications processor 180 and image processor 190 mayinclude a microprocessor, preprocessors (such as an image preprocessor),graphics processors, a central processing unit (CPU), support circuits,digital signal processors, integrated circuits, memory, or any othertypes of devices suitable for running applications and for imageprocessing and analysis. In some embodiments, applications processor 180and/or image processor 190 may include any type of single or multi-coreprocessor, mobile device microcontroller, central processing unit, etc.Various processing devices may be used, including, for example,processors available from manufacturers such as Intel®, AMD®, etc. andmay include various architectures (e.g., x86 processor, ARM®, etc.).

In some embodiments, applications processor 180 and/or image processor190 may include any of the EyeQ series of processor chips available fromMobileye®. These processor designs each include multiple processingunits with local memory and instruction sets. Such processors mayinclude video inputs for receiving image data from multiple imagesensors and may also include video out capabilities. In one example, theEyeQ2® uses 90 nm-micron technology operating at 332 Mhz. The EyeQ2®architecture consists of two floating point, hyper-thread 32-bit RISCCPUs (MIPS32® 34K® cores), five Vision Computing Engines (VCE), threeVector Microcode Processors (VMP®), Denali 64-bit Mobile DDR Controller,128-bit internal Sonics Interconnect, dual 16-bit Video input and 18-bitVideo output controllers, 16 channels DMA and several peripherals. TheMIPS34K CPU manages the five VCEs, three VMP™ and the DMA, the secondMIPS34K CPU and the multi-channel DMA as well as the other peripherals.The five VCEs, three VMP® and the MIPS34K CPU can perform intensivevision computations required by multi-function bundle applications. Inanother example, the EyeQ3®, which is a third generation processor andis six times more powerful that the EyeQ2®, may be used in the disclosedembodiments. In other examples, the EyeQ4® and/or the EyeQ5® may be usedin the disclosed embodiments. Of course, any newer or future EyeQprocessing devices may also be used together with the disclosedembodiments.

Any of the processing devices disclosed herein may be configured toperform certain functions. Configuring a processing device, such as anyof the described EyeQ processors or other controller or microprocessor,to perform certain functions may include programming of computerexecutable instructions and making those instructions available to theprocessing device for execution during operation of the processingdevice. In some embodiments, configuring a processing device may includeprogramming the processing device directly with architecturalinstructions. In other embodiments, configuring a processing device mayinclude storing executable instructions on a memory that is accessibleto the processing device during operation. For example, the processingdevice may access the memory to obtain and execute the storedinstructions during operation. In either case, the processing deviceconfigured to perform the sensing, image analysis, and/or navigationalfunctions disclosed herein represents a specialized hardware-basedsystem in control of multiple hardware based components of a hostvehicle.

While FIG. 1 depicts two separate processing devices included inprocessing unit 110, more or fewer processing devices may be used. Forexample, in some embodiments, a single processing device may be used toaccomplish the tasks of applications processor 180 and image processor190. In other embodiments, these tasks may be performed by more than twoprocessing devices. Further, in some embodiments, system 100 may includeone or more of processing unit 110 without including other components,such as image acquisition unit 120.

Processing unit 110 may comprise various types of devices. For example,processing unit 110 may include various devices, such as a controller,an image preprocessor, a central processing unit (CPU), supportcircuits, digital signal processors, integrated circuits, memory, or anyother types of devices for image processing and analysis. The imagepreprocessor may include a video processor for capturing, digitizing andprocessing the imagery from the image sensors. The CPU may comprise anynumber of microcontrollers or microprocessors. The support circuits maybe any number of circuits generally well known in the art, includingcache, power supply, clock and input-output circuits. The memory maystore software that, when executed by the processor, controls theoperation of the system. The memory may include databases and imageprocessing software. The memory may comprise any number of random accessmemories, read only memories, flash memories, disk drives, opticalstorage, tape storage, removable storage and other types of storage. Inone instance, the memory may be separate from the processing unit 110.In another instance, the memory may be integrated into the processingunit 110.

Each memory 140, 150 may include software instructions that whenexecuted by a processor (e.g., applications processor 180 and/or imageprocessor 190), may control operation of various aspects of system 100.These memory units may include various databases and image processingsoftware, as well as a trained system, such as a neural network, or adeep neural network, for example. The memory units may include randomaccess memory, read only memory, flash memory, disk drives, opticalstorage, tape storage, removable storage and/or any other types ofstorage. In some embodiments, memory units 140, 150 may be separate fromthe applications processor 180 and/or image processor 190. In otherembodiments, these memory units may be integrated into applicationsprocessor 180 and/or image processor 190.

Position sensor 130 may include any type of device suitable fordetermining a location associated with at least one component of system100. In some embodiments, position sensor 130 may include a GPSreceiver. Such receivers can determine a user position and velocity byprocessing signals broadcasted by global positioning system satellites.Position information from position sensor 130 may be made available toapplications processor 180 and/or image processor 190.

In some embodiments, system 100 may include components such as a speedsensor (e.g., a speedometer) for measuring a speed of vehicle 200.System 100 may also include one or more accelerometers (either singleaxis or multiaxis) for measuring accelerations of vehicle 200 along oneor more axes.

The memory units 140, 150 may include a database, or data organized inany other form, that indication a location of known landmarks. Sensoryinformation (such as images, radar signal, depth information from lidaror stereo processing of two or more images) of the environment may beprocessed together with position information, such as a GPS coordinate,vehicle's ego motion, etc. to determine a current location of thevehicle relative to the known landmarks, and refine the vehiclelocation. Certain aspects of this technology are included in alocalization technology known as REM™, which is being marketed by theassignee of the present application.

User interface 170 may include any device suitable for providinginformation to or for receiving inputs from one or more users of system100. In some embodiments, user interface 170 may include user inputdevices, including, for example, a touchscreen, microphone, keyboard,pointer devices, track wheels, cameras, knobs, buttons, etc. With suchinput devices, a user may be able to provide information inputs orcommands to system 100 by typing instructions or information, providingvoice commands, selecting menu options on a screen using buttons,pointers, or eye-tracking capabilities, or through any other suitabletechniques for communicating information to system 100.

User interface 170 may be equipped with one or more processing devicesconfigured to provide and receive information to or from a user andprocess that information for use by, for example, applications processor180. In some embodiments, such processing devices may executeinstructions for recognizing and tracking eye movements, receiving andinterpreting voice commands, recognizing and interpreting touches and/orgestures made on a touchscreen, responding to keyboard entries or menuselections, etc. In some embodiments, user interface 170 may include adisplay, speaker, tactile device, and/or any other devices for providingoutput information to a user.

Map database 160 may include any type of database for storing map datauseful to system 100. In some embodiments, map database 160 may includedata relating to the position, in a reference coordinate system, ofvarious items, including roads, water features, geographic features,businesses, points of interest, restaurants, gas stations, etc. Mapdatabase 160 may store not only the locations of such items, but alsodescriptors relating to those items, including, for example, namesassociated with any of the stored features. In some embodiments, mapdatabase 160 may be physically located with other components of system100. Alternatively or additionally, map database 160 or a portionthereof may be located remotely with respect to other components ofsystem 100 (e.g., processing unit 110). In such embodiments, informationfrom map database 160 may be downloaded over a wired or wireless dataconnection to a network (e.g., over a cellular network and/or theInternet, etc.). In some cases, map database 160 may store a sparse datamodel including polynomial representations of certain road features(e.g., lane markings) or target trajectories for the host vehicle. Mapdatabase 160 may also include stored representations of variousrecognized landmarks that may be used to determine or update a knownposition of the host vehicle with respect to a target trajectory. Thelandmark representations may include data fields such as landmark type,landmark location, among other potential identifiers.

Image capture devices 122, 124, and 126 may each include any type ofdevice suitable for capturing at least one image from an environment.Moreover, any number of image capture devices may be used to acquireimages for input to the image processor. Some embodiments may includeonly a single image capture device, while other embodiments may includetwo, three, or even four or more image capture devices. Image capturedevices 122, 124, and 126 will be further described with reference toFIGS. 2B-2E, below.

One or more cameras (e.g., image capture devices 122, 124, and 126) maybe part of a sensing block included on a vehicle. Various other sensorsmay be included in the sensing block, and any or all of the sensors maybe relied upon to develop a sensed navigational state of the vehicle. Inaddition to cameras (forward, sideward, rearward, etc), other sensorssuch as RADAR, LIDAR, and acoustic sensors may be included in thesensing block. Additionally, the sensing block may include one or morecomponents configured to communicate and transmit/receive informationrelating to the environment of the vehicle. For example, such componentsmay include wireless transceivers (RF, etc.) that may receive from asource remotely located with respect to the host vehicle sensor basedinformation or any other type of information relating to the environmentof the host vehicle. Such information may include sensor outputinformation, or related information, received from vehicle systems otherthan the host vehicle. In some embodiments, such information may includeinformation received from a remote computing device, a centralizedserver, etc. Furthermore, the cameras may take on many differentconfigurations: single camera units, multiple cameras, camera clusters,long FOV, short FOV, wide angle, fisheye, etc.

System 100, or various components thereof, may be incorporated intovarious different platforms. In some embodiments, system 100 may beincluded on a vehicle 200, as shown in FIG. 2A. For example, vehicle 200may be equipped with a processing unit 110 and any of the othercomponents of system 100, as described above relative to FIG. 1 . Whilein some embodiments vehicle 200 may be equipped with only a single imagecapture device (e.g., camera), in other embodiments, such as thosediscussed in connection with FIGS. 2B-2E, multiple image capture devicesmay be used. For example, either of image capture devices 122 and 124 ofvehicle 200, as shown in FIG. 2A, may be part of an ADAS (AdvancedDriver Assistance Systems) imaging set.

The image capture devices included on vehicle 200 as part of the imageacquisition unit 120 may be positioned at any suitable location. In someembodiments, as shown in FIGS. 2A-2E and 3A-3C, image capture device 122may be located in the vicinity of the rearview mirror. This position mayprovide a line of sight similar to that of the driver of vehicle 200,which may aid in determining what is and is not visible to the driver.Image capture device 122 may be positioned at any location near therearview mirror, but placing image capture device 122 on the driver sideof the mirror may further aid in obtaining images representative of thedriver's field of view and/or line of sight.

Other locations for the image capture devices of image acquisition unit120 may also be used. For example, image capture device 124 may belocated on or in a bumper of vehicle 200. Such a location may beespecially suitable for image capture devices having a wide field ofview. The line of sight of bumper-located image capture devices can bedifferent from that of the driver and, therefore, the bumper imagecapture device and driver may not always see the same objects. The imagecapture devices (e.g., image capture devices 122, 124, and 126) may alsobe located in other locations. For example, the image capture devicesmay be located on or in one or both of the side mirrors of vehicle 200,on the roof of vehicle 200, on the hood of vehicle 200, on the trunk ofvehicle 200, on the sides of vehicle 200, mounted on, positioned behind,or positioned in front of any of the windows of vehicle 200, and mountedin or near light fixtures on the front and/or back of vehicle 200, etc.

In addition to image capture devices, vehicle 200 may include variousother components of system 100. For example, processing unit 110 may beincluded on vehicle 200 either integrated with or separate from anengine control unit (ECU) of the vehicle. Vehicle 200 may also beequipped with a position sensor 130, such as a GPS receiver and may alsoinclude a map database 160 and memory units 140 and 150.

As discussed earlier, wireless transceiver 172 may and/or receive dataover one or more networks (e.g., cellular networks, the Internet, etc.).For example, wireless transceiver 172 may upload data collected bysystem 100 to one or more servers, and download data from the one ormore servers. Via wireless transceiver 172, system 100 may receive, forexample, periodic or on demand updates to data stored in map database160, memory 140, and/or memory 150. Similarly, wireless transceiver 172may upload any data (e.g., images captured by image acquisition unit120, data received by position sensor 130 or other sensors, vehiclecontrol systems, etc.) from system 100 and/or any data processed byprocessing unit 110 to the one or more servers.

System 100 may upload data to a server (e.g., to the cloud) based on aprivacy level setting. For example, system 100 may implement privacylevel settings to regulate or limit the types of data (includingmetadata) sent to the server that may uniquely identify a vehicle and ordriver/owner of a vehicle. Such settings may be set by user via, forexample, wireless transceiver 172, be initialized by factory defaultsettings, or by data received by wireless transceiver 172.

In some embodiments, system 100 may upload data according to a “high”privacy level, and under setting a setting, system 100 may transmit data(e.g., location information related to a route, captured images, etc.)without any details about the specific vehicle and/or driver/owner. Forexample, when uploading data according to a “high” privacy setting,system 100 may not include a vehicle identification number (VIN) or aname of a driver or owner of the vehicle, and may instead transmit data,such as captured images and/or limited location information related to aroute.

Other privacy levels are contemplated as well. For example, system 100may transmit data to a server according to an “intermediate” privacylevel and include additional information not included under a “high”privacy level, such as a make and/or model of a vehicle and/or a vehicletype (e.g., a passenger vehicle, sport utility vehicle, truck, etc.). Insome embodiments, system 100 may upload data according to a “low”privacy level. Under a “low” privacy level setting, system 100 mayupload data and include information sufficient to uniquely identify aspecific vehicle, owner/driver, and/or a portion or entirely of a routetraveled by the vehicle. Such “low” privacy level data may include oneor more of, for example, a VIN, a driver/owner name, an originationpoint of a vehicle prior to departure, an intended destination of thevehicle, a make and/or model of the vehicle, a type of the vehicle, etc.

FIG. 2A is a diagrammatic side view representation of an exemplaryvehicle imaging system consistent with the disclosed embodiments. FIG.2B is a diagrammatic top view illustration of the embodiment shown inFIG. 2A. As illustrated in FIG. 2B, the disclosed embodiments mayinclude a vehicle 200 including in its body a system 100 with a firstimage capture device 122 positioned in the vicinity of the rearviewmirror and/or near the driver of vehicle 200, a second image capturedevice 124 positioned on or in a bumper region (e.g., one of bumperregions 210) of vehicle 200, and a processing unit 110.

As illustrated in FIG. 2C, image capture devices 122 and 124 may both bepositioned in the vicinity of the rearview mirror and/or near the driverof vehicle 200. Additionally, while two image capture devices 122 and124 are shown in FIGS. 2B and 2C, it should be understood that otherembodiments may include more than two image capture devices. Forexample, in the embodiments shown in FIGS. 2D and 2E, first, second, andthird image capture devices 122, 124, and 126, are included in thesystem 100 of vehicle 200.

As illustrated in FIG. 2D, image capture device 122 may be positioned inthe vicinity of the rearview mirror and/or near the driver of vehicle200, and image capture devices 124 and 126 may be positioned on or in abumper region (e.g., one of bumper regions 210) of vehicle 200. And asshown in FIG. 2E, image capture devices 122, 124, and 126 may bepositioned in the vicinity of the rearview mirror and/or near the driverseat of vehicle 200. The disclosed embodiments are not limited to anyparticular number and configuration of the image capture devices, andthe image capture devices may be positioned in any appropriate locationwithin and/or on vehicle 200.

It is to be understood that the disclosed embodiments are not limited tovehicles and could be applied in other contexts. It is also to beunderstood that disclosed embodiments are not limited to a particulartype of vehicle 200 and may be applicable to all types of vehiclesincluding automobiles, trucks, trailers, and other types of vehicles.

The first image capture device 122 may include any suitable type ofimage capture device. Image capture device 122 may include an opticalaxis. In one instance, the image capture device 122 may include anAptina M9V024 WVGA sensor with a global shutter. In other embodiments,image capture device 122 may provide a resolution of 1280×960 pixels andmay include a rolling shutter. Image capture device 122 may includevarious optical elements. In some embodiments one or more lenses may beincluded, for example, to provide a desired focal length and field ofview for the image capture device. In some embodiments, image capturedevice 122 may be associated with a 6 mm lens or a 12 mm lens. In someembodiments, image capture device 122 may be configured to captureimages having a desired field-of-view (FOV) 202, as illustrated in FIG.2D. For example, image capture device 122 may be configured to have aregular FOV, such as within a range of 40 degrees to 56 degrees,including a 46 degree FOV, 50 degree FOV, 52 degree FOV, or greater.Alternatively, image capture device 122 may be configured to have anarrow FOV in the range of 23 to 40 degrees, such as a 28 degree FOV or36 degree FOV. In addition, image capture device 122 may be configuredto have a wide FOV in the range of 100 to 180 degrees. In someembodiments, image capture device 122 may include a wide angle bumpercamera or one with up to a 180 degree FOV. In some embodiments, imagecapture device 122 may be a 7.2 M pixel image capture device with anaspect ratio of about 2:1 (e.g., H×V=3800×1900 pixels) with about 100degree horizontal FOV. Such an image capture device may be used in placeof a three image capture device configuration. Due to significant lensdistortion, the vertical FOV of such an image capture device may besignificantly less than 50 degrees in implementations in which the imagecapture device uses a radially symmetric lens. For example, such a lensmay not be radially symmetric which would allow for a vertical FOVgreater than 50 degrees with 100 degree horizontal FOV.

The first image capture device 122 may acquire a plurality of firstimages relative to a scene associated with vehicle 200. Each of theplurality of first images may be acquired as a series of image scanlines, which may be captured using a rolling shutter. Each scan line mayinclude a plurality of pixels.

The first image capture device 122 may have a scan rate associated withacquisition of each of the first series of image scan lines. The scanrate may refer to a rate at which an image sensor can acquire image dataassociated with each pixel included in a particular scan line.

Image capture devices 122, 124, and 126 may contain any suitable typeand number of image sensors, including CCD sensors or CMOS sensors, forexample. In one embodiment, a CMOS image sensor may be employed alongwith a rolling shutter, such that each pixel in a row is read one at atime, and scanning of the rows proceeds on a row-by-row basis until anentire image frame has been captured. In some embodiments, the rows maybe captured sequentially from top to bottom relative to the frame.

In some embodiments, one or more of the image capture devices (e.g.,image capture devices 122, 124, and 126) disclosed herein may constitutea high resolution imager and may have a resolution greater than 5 Mpixel, 7 M pixel, 10 M pixel, or greater.

The use of a rolling shutter may result in pixels indifferent rows beingexposed and captured at different times, which may cause skew and otherimage artifacts in the captured image frame. On the other hand, when theimage capture device 122 is configured to operate with a global orsynchronous shutter, all of the pixels may be exposed for the sameamount of time and during a common exposure period. As a result, theimage data in a frame collected from a system employing a global shutterrepresents a snapshot of the entire FOV (such as FOV 202) at aparticular time. In contrast, in a rolling shutter application, each rowin a frame is exposed and data is capture at different times. Thus,moving objects may appear distorted in an image capture device having arolling shutter. This phenomenon will be described in greater detailbelow.

The second image capture device 124 and the third image capturing device126 may be any type of image capture device. Like the first imagecapture device 122, each of image capture devices 124 and 126 mayinclude an optical axis. In one embodiment, each of image capturedevices 124 and 126 may include an Aptina M9V024 WVGA sensor with aglobal shutter. Alternatively, each of image capture devices 124 and 126may include a rolling shutter. Like image capture device 122, imagecapture devices 124 and 126 may be configured to include various lensesand optical elements. In some embodiments, lenses associated with imagecapture devices 124 and 126 may provide FOVs (such as FOVs 204 and 206)that are the same as, or narrower than, a FOV (such as FOV 202)associated with image capture device 122. For example, image capturedevices 124 and 126 may have FOVs of 40 degrees, 30 degrees, 26 degrees,23 degrees, 20 degrees, or less.

Image capture devices 124 and 126 may acquire a plurality of second andthird images relative to a scene associated with vehicle 200. Each ofthe plurality of second and third images may be acquired as a second andthird series of image scan lines, which may be captured using a rollingshutter. Each scan line or row may have a plurality of pixels. Imagecapture devices 124 and 126 may have second and third scan ratesassociated with acquisition of each of image scan lines included in thesecond and third series.

Each image capture device 122, 124, and 126 may be positioned at anysuitable position and orientation relative to vehicle 200. The relativepositioning of the image capture devices 122, 124, and 126 may beselected to aid in fusing together the information acquired from theimage capture devices. For example, in some embodiments, a FOV (such asFOV 204) associated with image capture device 124 may overlap partiallyor fully with a FOV (such as FOV 202) associated with image capturedevice 122 and a FOV (such as FOV 206) associated with image capturedevice 126.

Image capture devices 122, 124, and 126 may be located on vehicle 200 atany suitable relative heights. In one instance, there may be a heightdifference between the image capture devices 122, 124, and 126, whichmay provide sufficient parallax information to enable stereo analysis.For example, as shown in FIG. 2A, the two image capture devices 122 and124 are at different heights. There may also be a lateral displacementdifference between image capture devices 122, 124, and 126, givingadditional parallax information for stereo analysis by processing unit110, for example. The difference in the lateral displacement may bedenoted by dx, as shown in FIGS. 2C and 2D. In some embodiments, fore oraft displacement (e.g., range displacement) may exist between imagecapture devices 122, 124, and 126. For example, image capture device 122may be located 0.5 to 2 meters or more behind image capture device 124and/or image capture device 126. This type of displacement may enableone of the image capture devices to cover potential blind spots of theother image capture device(s).

Image capture devices 122 may have any suitable resolution capability(e.g., number of pixels associated with the image sensor), and theresolution of the image sensor(s) associated with the image capturedevice 122 may be higher, lower, or the same as the resolution of theimage sensor(s) associated with image capture devices 124 and 126. Insome embodiments, the image sensor(s) associated with image capturedevice 122 and/or image capture devices 124 and 126 may have aresolution of 640×480, 1024×768, 1280×960, or any other suitableresolution.

The frame rate (e.g., the rate at which an image capture device acquiresa set of pixel data of one image frame before moving on to capture pixeldata associated with the next image frame) may be controllable. Theframe rate associated with image capture device 122 may be higher,lower, or the same as the frame rate associated with image capturedevices 124 and 126. The frame rate associated with image capturedevices 122, 124, and 126 may depend on a variety of factors that mayaffect the timing of the frame rate. For example, one or more of imagecapture devices 122, 124, and 126 may include a selectable pixel delayperiod imposed before or after acquisition of image data associated withone or more pixels of an image sensor in image capture device 122, 124,and/or 126. Generally, image data corresponding to each pixel may beacquired according to a clock rate for the device (e.g., one pixel perclock cycle). Additionally, in embodiments including a rolling shutter,one or more of image capture devices 122, 124, and 126 may include aselectable horizontal blanking period imposed before or afteracquisition of image data associated with a row of pixels of an imagesensor in image capture device 122, 124, and/or 126. Further, one ormore of image capture devices 122, 124, and/or 126 may include aselectable vertical blanking period imposed before or after acquisitionof image data associated with an image frame of image capture device122, 124, and 126.

These timing controls may enable synchronization of frame ratesassociated with image capture devices 122, 124, and 126, even where theline scan rates of each are different. Additionally, as will bediscussed in greater detail below, these selectable timing controls,among other factors (e.g., image sensor resolution, maximum line scanrates, etc.) may enable synchronization of image capture from an areawhere the FOV of image capture device 122 overlaps with one or more FOVsof image capture devices 124 and 126, even where the field of view ofimage capture device 122 is different from the FOVs of image capturedevices 124 and 126.

Frame rate timing in image capture device 122, 124, and 126 may dependon the resolution of the associated image sensors. For example, assumingsimilar line scan rates for both devices, if one device includes animage sensor having a resolution of 640×480 and another device includesan image sensor with a resolution of 1280×960, then more time will berequired to acquire a frame of image data from the sensor having thehigher resolution.

Another factor that may affect the timing of image data acquisition inimage capture devices 122, 124, and 126 is the maximum line scan rate.For example, acquisition of a row of image data from an image sensorincluded in image capture device 122, 124, and 126 will require someminimum amount of time. Assuming no pixel delay periods are added, thisminimum amount of time for acquisition of a row of image data will berelated to the maximum line scan rate for a particular device. Devicesthat offer higher maximum line scan rates have the potential to providehigher frame rates than devices with lower maximum line scan rates. Insome embodiments, one or more of image capture devices 124 and 126 mayhave a maximum line scan rate that is higher than a maximum line scanrate associated with image capture device 122. In some embodiments, themaximum line scan rate of image capture device 124 and/or 126 may be1.25, 1.5, 1.75, or 2 times or more than a maximum line scan rate ofimage capture device 122.

In another embodiment, image capture devices 122, 124, and 126 may havethe same maximum line scan rate, but image capture device 122 may beoperated at a scan rate less than or equal to its maximum scan rate. Thesystem may be configured such that one or more of image capture devices124 and 126 operate at a line scan rate that is equal to the line scanrate of image capture device 122. In other instances, the system may beconfigured such that the line scan rate of image capture device 124and/or image capture device 126 may be 1.25, 1.5, 1.75, or 2 times ormore than the line scan rate of image capture device 122.

In some embodiments, image capture devices 122, 124, and 126 may beasymmetric. That is, they may include cameras having different fields ofview (FOV) and focal lengths. The fields of view of image capturedevices 122, 124, and 126 may include any desired area relative to anenvironment of vehicle 200, for example. In some embodiments, one ormore of image capture devices 122, 124, and 126 may be configured toacquire image data from an environment in front of vehicle 200, behindvehicle 200, to the sides of vehicle 200, or combinations thereof.

Further, the focal length associated with each image capture device 122,124, and/or 126 may be selectable (e.g., by inclusion of appropriatelenses etc.) such that each device acquires images of objects at adesired distance range relative to vehicle 200. For example, in someembodiments image capture devices 122, 124, and 126 may acquire imagesof close-up objects within a few meters from the vehicle. Image capturedevices 122, 124, and 126 may also be configured to acquire images ofobjects at ranges more distant from the vehicle (e.g., 25 m, 50 m, 100m, 150 m, or more). Further, the focal lengths of image capture devices122, 124, and 126 may be selected such that one image capture device(e.g., image capture device 122) can acquire images of objectsrelatively close to the vehicle (e.g., within 10 m or within 20 m) whilethe other image capture devices (e.g., image capture devices 124 and126) can acquire images of more distant objects (e.g., greater than 20m, 50 m, 100 m, 150 m, etc.) from vehicle 200.

According to some embodiments, the FOV of one or more image capturedevices 122, 124, and 126 may have a wide angle. For example, it may beadvantageous to have a FOV of 140 degrees, especially for image capturedevices 122, 124, and 126 that may be used to capture images of the areain the vicinity of vehicle 200. For example, image capture device 122may be used to capture images of the area to the right or left ofvehicle 200 and, in such embodiments, it may be desirable for imagecapture device 122 to have a wide FOV (e.g., at least 140 degrees).

The field of view associated with each of image capture devices 122,124, and 126 may depend on the respective focal lengths. For example, asthe focal length increases, the corresponding field of view decreases.

Image capture devices 122, 124, and 126 may be configured to have anysuitable fields of view. In one particular example, image capture device122 may have a horizontal FOV of 46 degrees, image capture device 124may have a horizontal FOV of 23 degrees, and image capture device 126may have a horizontal FOV in between 23 and 46 degrees. In anotherinstance, image capture device 122 may have a horizontal FOV of 52degrees, image capture device 124 may have a horizontal FOV of 26degrees, and image capture device 126 may have a horizontal FOV inbetween 26 and 52 degrees. In some embodiments, a ratio of the FOV ofimage capture device 122 to the FOVs of image capture device 124 and/orimage capture device 126 may vary from 1.5 to 2.0. In other embodiments,this ratio may vary between 1.25 and 2.25.

System 100 may be configured so that afield of view of image capturedevice 122 overlaps, at least partially or fully, with a field of viewof image capture device 124 and/or image capture device 126. In someembodiments, system 100 may be configured such that the fields of viewof image capture devices 124 and 126, for example, fall within (e.g.,are narrower than) and share a common center with the field of view ofimage capture device 122. In other embodiments, the image capturedevices 122, 124, and 126 may capture adjacent FOVs or may have partialoverlap in their FOVs. In some embodiments, the fields of view of imagecapture devices 122, 124, and 126 may be aligned such that a center ofthe narrower FOV image capture devices 124 and/or 126 may be located ina lower half of the field of view of the wider FOV device 122.

FIG. 2F is a diagrammatic representation of exemplary vehicle controlsystems, consistent with the disclosed embodiments. As indicated in FIG.2F, vehicle 200 may include throttling system 220, braking system 230,and steering system 240. System 100 may provide inputs (e.g., controlsignals) to one or more of throttling system 220, braking system 230,and steering system 240 over one or more data links (e.g., any wiredand/or wireless link or links for transmitting data). For example, basedon analysis of images acquired by image capture devices 122, 124, and/or126, system 100 may provide control signals to one or more of throttlingsystem 220, braking system 230, and steering system 240 to navigatevehicle 200 (e.g., by causing an acceleration, a turn, a lane shift,etc.). Further, system 100 may receive inputs from one or more ofthrottling system 220, braking system 230, and steering system 24indicating operating conditions of vehicle 200 (e.g., speed, whethervehicle 200 is braking and/or turning, etc.). Further details areprovided in connection with FIGS. 4-7 , below.

As shown in FIG. 3A, vehicle 200 may also include a user interface 170for interacting with a driver or a passenger of vehicle 200. Forexample, user interface 170 in a vehicle application may include a touchscreen 320, knobs 330, buttons 340, and a microphone 350. A driver orpassenger of vehicle 200 may also use handles (e.g., located on or nearthe steering column of vehicle 200 including, for example, turn signalhandles), buttons (e.g., located on the steering wheel of vehicle 200),and the like, to interact with system 100. In some embodiments,microphone 350 may be positioned adjacent to a rearview mirror 310.Similarly, in some embodiments, image capture device 122 may be locatednear rearview mirror 310. In some embodiments, user interface 170 mayalso include one or more speakers 360 (e.g., speakers of a vehicle audiosystem). For example, system 100 may provide various notifications(e.g., alerts) via speakers 360.

FIGS. 3B-3D are illustrations of an exemplary camera mount 370configured to be positioned behind a rearview mirror (e.g., rearviewmirror 310) and against a vehicle windshield, consistent with disclosedembodiments. As shown in FIG. 3B, camera mount 370 may include imagecapture devices 122, 124, and 126. Image capture devices 124 and 126 maybe positioned behind a glare shield 380, which may be flush against thevehicle windshield and include a composition of film and/oranti-reflective materials. For example, glare shield 380 may bepositioned such that it aligns against a vehicle windshield having amatching slope. In some embodiments, each of image capture devices 122,124, and 126 may be positioned behind glare shield 380, as depicted, forexample, in FIG. 3D. The disclosed embodiments are not limited to anyparticular configuration of image capture devices 122, 124, and 126,camera mount 370, and glare shield 380. FIG. 3C is an illustration ofcamera mount 370 shown in FIG. 3B from a front perspective.

As will be appreciated by a person skilled in the art having the benefitof this disclosure, numerous variations and/or modifications may be madeto the foregoing disclosed embodiments. For example, not all componentsare essential for the operation of system 100. Further, any componentmay be located in any appropriate part of system 100 and the componentsmay be rearranged into a variety of configurations while providing thefunctionality of the disclosed embodiments. Therefore, the foregoingconfigurations are examples and, regardless of the configurationsdiscussed above, system 100 can provide a wide range of functionality toanalyze the surroundings of vehicle 200 and navigate vehicle 200 inresponse to the analysis.

As discussed below in further detail and consistent with variousdisclosed embodiments, system 100 may provide a variety of featuresrelated to autonomous driving and/or driver assist technology. Forexample, system 100 may analyze image data, position data (e.g., GPSlocation information), map data, speed data, and/or data from sensorsincluded in vehicle 200. System 100 may collect the data for analysisfrom, for example, image acquisition unit 120, position sensor 130, andother sensors. Further, system 100 may analyze the collected data todetermine whether or not vehicle 200 should take a certain action, andthen automatically take the determined action without humanintervention. For example, when vehicle 200 navigates without humanintervention, system 100 may automatically control the braking,acceleration, and/or steering of vehicle 200 (e.g., by sending controlsignals to one or more of throttling system 220, braking system 230, andsteering system 240). Further, system 100 may analyze the collected dataand issue warnings and/or alerts to vehicle occupants based on theanalysis of the collected data. Additional details regarding the variousembodiments that are provided by system 100 are provided below.

Forward-Facing Multi-Imaging System

As discussed above, system 100 may provide drive assist functionalitythat uses a multi-camera system. The multi-camera system may use one ormore cameras facing in the forward direction of a vehicle. In otherembodiments, the multi-camera system may include one or more camerasfacing to the side of a vehicle or to the rear of the vehicle. In oneembodiment, for example, system 100 may use a two-camera imaging system,where a first camera and a second camera (e.g., image capture devices122 and 124) may be positioned at the front and/or the sides of avehicle (e.g., vehicle 200). Other camera configurations are consistentwith the disclosed embodiments, and the configurations disclosed hereinare examples. For example, system 100 may include a configuration of anynumber of cameras (e.g., one, two, three, four, five, six, seven, eight,etc.) Furthermore, system 100 may include “clusters” of cameras. Forexample, a cluster of cameras (including any appropriate number ofcameras, e.g., one, four, eight, etc.) may be forward-facing relative toa vehicle, or may be facing any other direction (e.g., reward-facing,side-facing, at an angle, etc.) Accordingly, system 100 may includemultiple clusters of cameras, with each cluster oriented in a particulardirection to capture images from a particular region of a vehicle'senvironment.

The first camera may have afield of view that is greater than, lessthan, or partially overlapping with, the field of view of the secondcamera. In addition, the first camera may be connected to a first imageprocessor to perform monocular image analysis of images provided by thefirst camera, and the second camera may be connected to a second imageprocessor to perform monocular image analysis of images provided by thesecond camera. The outputs (e.g., processed information) of the firstand second image processors may be combined. In some embodiments, thesecond image processor may receive images from both the first camera andsecond camera to perform stereo analysis. In another embodiment, system100 may use a three-camera imaging system where each of the cameras hasa different field of view. Such a system may, therefore, make decisionsbased on information derived from objects located at varying distancesboth forward and to the sides of the vehicle. References to monocularimage analysis may refer to instances where image analysis is performedbased on images captured from a single point of view (e.g., from asingle camera). Stereo image analysis may refer to instances where imageanalysis is performed based on two or more images captured with one ormore variations of an image capture parameter. For example, capturedimages suitable for performing stereo image analysis may include imagescaptured: from two or more different positions, from different fields ofview, using different focal lengths, along with parallax information,etc.

For example, in one embodiment, system 100 may implement a three cameraconfiguration using image capture devices 122-126. In such aconfiguration, image capture device 122 may provide a narrow field ofview (e.g., 34 degrees, or other values selected from a range of about20 to 45 degrees, etc.), image capture device 124 may provide a widefield of view (e.g., 150 degrees or other values selected from a rangeof about 100 to about 180 degrees), and image capture device 126 mayprovide an intermediate field of view (e.g., 46 degrees or other valuesselected from a range of about 35 to about 60 degrees). In someembodiments, image capture device 126 may act as a main or primarycamera. Image capture devices 122-126 may be positioned behind rearviewmirror 310 and positioned substantially side-by-side (e.g., 6 cm apart).Further, in some embodiments, as discussed above, one or more of imagecapture devices 122-126 may be mounted behind glare shield 380 that isflush with the windshield of vehicle 200. Such shielding may act tominimize the impact of any reflections from inside the car on imagecapture devices 122-126.

In another embodiment, as discussed above in connection with FIGS. 3Band 3C, the wide field of view camera (e.g., image capture device 124 inthe above example) may be mounted lower than the narrow and main fieldof view cameras (e.g., image devices 122 and 126 in the above example).This configuration may provide a free line of sight from the wide fieldof view camera. To reduce reflections, the cameras may be mounted closeto the windshield of vehicle 200, and may include polarizers on thecameras to damp reflected light.

A three camera system may provide certain performance characteristics.For example, some embodiments may include an ability to validate thedetection of objects by one camera based on detection results fromanother camera. In the three camera configuration discussed above,processing unit 110 may include, for example, three processing devices(e.g., three EyeQ series of processor chips, as discussed above), witheach processing device dedicated to processing images captured by one ormore of image capture devices 122-126.

Ina three camera system, a first processing device may receive imagesfrom both the main camera and the narrow field of view camera, andperform vision processing of the narrow FOV camera to, for example,detect other vehicles, pedestrians, lane marks, traffic signs, trafficlights, and other road objects. Further, the first processing device maycalculate a disparity of pixels between the images from the main cameraand the narrow camera and create a 3D reconstruction of the environmentof vehicle 200. The first processing device may then combine the 3Dreconstruction with 3D map data or with 3D information calculated basedon information from another camera.

The second processing device may receive images from the main camera andperform vision processing to detect other vehicles, pedestrians, lanemarks, traffic signs, traffic lights, and other road objects.Additionally, the second processing device may calculate a cameradisplacement and, based on the displacement, calculate a disparity ofpixels between successive images and create a 3D reconstruction of thescene (e.g., a structure from motion). The second processing device maysend the structure from motion based 3D reconstruction to the firstprocessing device to be combined with the stereo 3D images.

The third processing device may receive images from the wide FOV cameraand process the images to detect vehicles, pedestrians, lane marks,traffic signs, traffic lights, and other road objects. The thirdprocessing device may further execute additional processing instructionsto analyze images to identify objects moving in the image, such asvehicles changing lanes, pedestrians, etc.

In some embodiments, having streams of image-based information capturedand processed independently may provide an opportunity for providingredundancy in the system. Such redundancy may include, for example,using a first image capture device and the images processed from thatdevice to validate and/or supplement information obtained by capturingand processing image information from at least a second image capturedevice.

In some embodiments, system 100 may use two image capture devices (e.g.,image capture devices 122 and 124) in providing navigation assistancefor vehicle 200 and use a third image capture device (e.g., imagecapture device 126) to provide redundancy and validate the analysis ofdata received from the other two image capture devices. For example, insuch a configuration, image capture devices 122 and 124 may provideimages for stereo analysis by system 100 for navigating vehicle 200,while image capture device 126 may provide images for monocular analysisby system 100 to provide redundancy and validation of informationobtained based on images captured from image capture device 122 and/orimage capture device 124. That is, image capture device 126 (and acorresponding processing device) may be considered to provide aredundant sub-system for providing a check on the analysis derived fromimage capture devices 122 and 124 (e.g., to provide an automaticemergency braking (AEB) system). Furthermore, in some embodiments,redundancy and validation of received data may be supplemented based oninformation received from one more sensors (e.g., radar, lidar, acousticsensors, information received from one or more transceivers outside of avehicle, etc.).

One of skill in the art will recognize that the above cameraconfigurations, camera placements, number of cameras, camera locations,etc., are examples only. These components and others described relativeto the overall system may be assembled and used in a variety ofdifferent configurations without departing from the scope of thedisclosed embodiments. Further details regarding usage of a multi-camerasystem to provide driver assist and/or autonomous vehicle functionalityfollow below.

FIG. 4 is an exemplary functional block diagram of memory 140 and/or150, which may be stored/programmed with instructions for performing oneor more operations consistent with the disclosed embodiments. Althoughthe following refers to memory 140, one of skill in the art willrecognize that instructions may be stored in memory 140 and/or 150.

As shown in FIG. 4 , memory 140 may store a monocular image analysismodule 402, a stereo image analysis module 404, a velocity andacceleration module 406, and a navigational response module 408. Thedisclosed embodiments are not limited to any particular configuration ofmemory 140. Further, applications processor 180 and/or image processor190 may execute the instructions stored in any of modules 402-408included in memory 140. One of skill in the art will understand thatreferences in the following discussions to processing unit 110 may referto applications processor 180 and image processor 190 individually orcollectively. Accordingly, steps of any of the following processes maybe performed by one or more processing devices.

In one embodiment, monocular image analysis module 402 may storeinstructions (such as computer vision software) which, when executed byprocessing unit 110, performs monocular image analysis of a set ofimages acquired by one of image capture devices 122, 124, and 126. Insome embodiments, processing unit 110 may combine information from a setof images with additional sensory information (e.g., information fromradar) to perform the monocular image analysis. As described inconnection with FIGS. 5A-5D below, monocular image analysis module 402may include instructions for detecting a set of features within the setof images, such as lane markings, vehicles, pedestrians, road signs,highway exit ramps, traffic lights, hazardous objects, and any otherfeature associated with an environment of a vehicle. Based on theanalysis, system 100 (e.g., via processing unit 110) may cause one ormore navigational responses in vehicle 200, such as a turn, a laneshift, a change in acceleration, and the like, as discussed below inconnection with navigational response module 408.

In one embodiment, monocular image analysis module 402 may storeinstructions (such as computer vision software) which, when executed byprocessing unit 110, performs monocular image analysis of a set ofimages acquired by one of image capture devices 122, 124, and 126. Insome embodiments, processing unit 110 may combine information from a setof images with additional sensory information (e.g., information fromradar, lidar, etc.) to perform the monocular image analysis. Asdescribed in connection with FIGS. 5A-5D below, monocular image analysismodule 402 may include instructions for detecting a set of featureswithin the set of images, such as lane markings, vehicles, pedestrians,road signs, highway exit ramps, traffic lights, hazardous objects, andany other feature associated with an environment of a vehicle. Based onthe analysis, system 100 (e.g., via processing unit 110) may cause oneor more navigational responses in vehicle 200, such as a turn, a laneshift, a change in acceleration, and the like, as discussed below inconnection with determining a navigational response.

In one embodiment, stereo image analysis module 404 may storeinstructions (such as computer vision software) which, when executed byprocessing unit 110, performs stereo image analysis of first and secondsets of images acquired by a combination of image capture devicesselected from any of image capture devices 122, 124, and 126. In someembodiments, processing unit 110 may combine information from the firstand second sets of images with additional sensory information (e.g.,information from radar) to perform the stereo image analysis. Forexample, stereo image analysis module 404 may include instructions forperforming stereo image analysis based on a first set of images acquiredby image capture device 124 and a second set of images acquired by imagecapture device 126. As described in connection with FIG. 6 below, stereoimage analysis module 404 may include instructions for detecting a setof features within the first and second sets of images, such as lanemarkings, vehicles, pedestrians, road signs, highway exit ramps, trafficlights, hazardous objects, and the like. Based on the analysis,processing unit 110 may cause one or more navigational responses invehicle 200, such as a turn, a lane shift, a change in acceleration, andthe like, as discussed below in connection with navigational responsemodule 408. Furthermore, in some embodiments, stereo image analysismodule 404 may implement techniques associated with a trained system(such as a neural network or a deep neural network) or an untrainedsystem.

In one embodiment, velocity and acceleration module 406 may storesoftware configured to analyze data received from one or more computingand electromechanical devices in vehicle 200 that are configured tocause a change in velocity and/or acceleration of vehicle 200. Forexample, processing unit 110 may execute instructions associated withvelocity and acceleration module 406 to calculate a target speed forvehicle 200 based on data derived from execution of monocular imageanalysis module 402 and/or stereo image analysis module 404. Such datamay include, for example, a target position, velocity, and/oracceleration, the position and/or speed of vehicle 200 relative to anearby vehicle, pedestrian, or road object, position information forvehicle 200 relative to lane markings of the road, and the like. Inaddition, processing unit 110 may calculate a target speed for vehicle200 based on sensory input (e.g., information from radar) and input fromother systems of vehicle 200, such as throttling system 220, brakingsystem 230, and/or steering system 240 of vehicle 200. Based on thecalculated target speed, processing unit 110 may transmit electronicsignals to throttling system 220, braking system 230, and/or steeringsystem 240 of vehicle 200 to trigger a change in velocity and/oracceleration by, for example, physically depressing the brake or easingup off the accelerator of vehicle 200.

In one embodiment, navigational response module 408 may store softwareexecutable by processing unit 110 to determine a desired navigationalresponse based on data derived from execution of monocular imageanalysis module 402 and/or stereo image analysis module 404. Such datamay include position and speed information associated with nearbyvehicles, pedestrians, and road objects, target position information forvehicle 200, and the like. Additionally, in some embodiments, thenavigational response may be based (partially or fully) on map data, apredetermined position of vehicle 200, and/or a relative velocity or arelative acceleration between vehicle 200 and one or more objectsdetected from execution of monocular image analysis module 402 and/orstereo image analysis module 404. Navigational response module 408 mayalso determine a desired navigational response based on sensory input(e.g., information from radar) and inputs from other systems of vehicle200, such as throttling system 220, braking system 230, and steeringsystem 240 of vehicle 200. Based on the desired navigational response,processing unit 110 may transmit electronic signals to throttling system220, braking system 230, and steering system 240 of vehicle 200 totrigger a desired navigational response by, for example, turning thesteering wheel of vehicle 200 to achieve a rotation of a predeterminedangle. In some embodiments, processing unit 110 may use the output ofnavigational response module 408 (e.g., the desired navigationalresponse) as an input to execution of velocity and acceleration module406 for calculating a change in speed of vehicle 200.

Furthermore, any of the modules (e.g., modules 402, 404, and 406)disclosed herein may implement techniques associated with a trainedsystem (such as a neural network or a deep neural network) or anuntrained system.

FIG. 5A is a flowchart showing an exemplary process 500A for causing oneor more navigational responses based on monocular image analysis,consistent with disclosed embodiments. At step 510, processing unit 110may receive a plurality of images via data interface 128 betweenprocessing unit 110 and image acquisition unit 120. For instance, acamera included in image acquisition unit 120 (such as image capturedevice 122 having field of view 202) may capture a plurality of imagesof an area forward of vehicle 200 (or to the sides or rear of a vehicle,for example) and transmit them over a data connection (e.g., digital,wired, USB, wireless, Bluetooth, etc.) to processing unit 110.Processing unit 110 may execute monocular image analysis module 402 toanalyze the plurality of images at step 520, as described in furtherdetail in connection with FIGS. 5B-5D below. By performing the analysis,processing unit 110 may detect a set of features within the set ofimages, such as lane markings, vehicles, pedestrians, road signs,highway exit ramps, traffic lights, and the like.

Processing unit 110 may also execute monocular image analysis module 402to detect various road hazards at step 520, such as, for example, partsof a truck tire, fallen road signs, loose cargo, small animals, and thelike. Road hazards may vary in structure, shape, size, and color, whichmay make detection of such hazards more challenging. In someembodiments, processing unit 110 may execute monocular image analysismodule 402 to perform multi-frame analysis on the plurality of images todetect road hazards. For example, processing unit 110 may estimatecamera motion between consecutive image frames and calculate thedisparities in pixels between the frames to construct a 3D-map of theroad. Processing unit 110 may then use the 3D-map to detect the roadsurface, as well as hazards existing above the road surface.

At step 530, processing unit 110 may execute navigational responsemodule 408 to cause one or more navigational responses in vehicle 200based on the analysis performed at step 520 and the techniques asdescribed above in connection with FIG. 4 . Navigational responses mayinclude, for example, a turn, a lane shift, a change in acceleration,and the like. In some embodiments, processing unit 110 may use dataderived from execution of velocity and acceleration module 406 to causethe one or more navigational responses. Additionally, multiplenavigational responses may occur simultaneously, in sequence, or anycombination thereof. For instance, processing unit 110 may cause vehicle200 to shift one lane over and then accelerate by, for example,sequentially transmitting control signals to steering system 240 andthrottling system 220 of vehicle 200. Alternatively, processing unit 110may cause vehicle 200 to brake while at the same time shifting lanes by,for example, simultaneously transmitting control signals to brakingsystem 230 and steering system 240 of vehicle 200.

FIG. 5B is a flowchart showing an exemplary process 500B for detectingone or more vehicles and/or pedestrians in a set of images, consistentwith disclosed embodiments. Processing unit 110 may execute monocularimage analysis module 402 to implement process 500B. At step 540,processing unit 110 may determine a set of candidate objectsrepresenting possible vehicles and/or pedestrians. For example,processing unit 110 may scan one or more images, compare the images toone or more predetermined patterns, and identify within each imagepossible locations that may contain objects of interest (e.g., vehicles,pedestrians, or portions thereof). The predetermined patterns may bedesigned in such a way to achieve a high rate of “false hits” and a lowrate of “misses.” For example, processing unit 110 may use a lowthreshold of similarity to predetermined patterns for identifyingcandidate objects as possible vehicles or pedestrians. Doing so mayallow processing unit 110 to reduce the probability of missing (e.g.,not identifying) a candidate object representing a vehicle orpedestrian.

At step 542, processing unit 110 may filter the set of candidate objectsto exclude certain candidates (e.g., irrelevant or less relevantobjects) based on classification criteria. Such criteria may be derivedfrom various properties associated with object types stored in adatabase (e.g., a database stored in memory 140). Properties may includeobject shape, dimensions, texture, position (e.g., relative to vehicle200), and the like. Thus, processing unit 110 may use one or more setsof criteria to reject false candidates from the set of candidateobjects.

At step 544, processing unit 110 may analyze multiple frames of imagesto determine whether objects in the set of candidate objects representvehicles and/or pedestrians. For example, processing unit 110 may tracka detected candidate object across consecutive frames and accumulateframe-by-frame data associated with the detected object (e.g., size,position relative to vehicle 200, etc.). Additionally, processing unit110 may estimate parameters for the detected object and compare theobject's frame-by-frame position data to a predicted position.

At step 546, processing unit 110 may construct a set of measurements forthe detected objects. Such measurements may include, for example,position, velocity, and acceleration values (relative to vehicle 200)associated with the detected objects. In some embodiments, processingunit 110 may construct the measurements based on estimation techniquesusing a series of time-based observations such as Kalman filters orlinear quadratic estimation (LQE), and/or based on available modelingdata for different object types (e.g., cars, trucks, pedestrians,bicycles, road signs, etc.). The Kalman filters may be based on ameasurement of an object's scale, where the scale measurement isproportional to a time to collision (e.g., the amount of time forvehicle 200 to reach the object). Thus, by performing steps 540-546,processing unit 110 may identify vehicles and pedestrians appearingwithin the set of captured images and derive information (e.g.,position, speed, size) associated with the vehicles and pedestrians.Based on the identification and the derived information, processing unit110 may cause one or more navigational responses in vehicle 200, asdescribed in connection with FIG. 5A, above.

At step 548, processing unit 110 may perform an optical flow analysis ofone or more images to reduce the probabilities of detecting a “falsehit” and missing a candidate object that represents a vehicle orpedestrian. The optical flow analysis may refer to, for example,analyzing motion patterns relative to vehicle 200 in the one or moreimages associated with other vehicles and pedestrians, and that aredistinct from road surface motion. Processing unit 110 may calculate themotion of candidate objects by observing the different positions of theobjects across multiple image frames, which are captured at differenttimes. Processing unit 110 may use the position and time values asinputs into mathematical models for calculating the motion of thecandidate objects. Thus, optical flow analysis may provide anothermethod of detecting vehicles and pedestrians that are nearby vehicle200. Processing unit 110 may perform optical flow analysis incombination with steps 540-546 to provide redundancy for detectingvehicles and pedestrians and increase the reliability of system 100.

FIG. 5C is a flowchart showing an exemplary process 500C for detectingroad marks and/or lane geometry information in a set of images,consistent with disclosed embodiments. Processing unit 110 may executemonocular image analysis module 402 to implement process 500C. At step550, processing unit 110 may detect a set of objects by scanning one ormore images. To detect segments of lane markings, lane geometryinformation, and other pertinent road marks, processing unit 110 mayfilter the set of objects to exclude those determined to be irrelevant(e.g., minor potholes, small rocks, etc.). At step 552, processing unit110 may group together the segments detected in step 550 belonging tothe same road mark or lane mark. Based on the grouping, processing unit110 may develop a model to represent the detected segments, such as amathematical model.

At step 554, processing unit 110 may construct a set of measurementsassociated with the detected segments. In some embodiments, processingunit 110 may create a projection of the detected segments from the imageplane onto the real-world plane. The projection may be characterizedusing a 3rd-degree polynomial having coefficients corresponding tophysical properties such as the position, slope, curvature, andcurvature derivative of the detected road. In generating the projection,processing unit 110 may take into account changes in the road surface,as well as pitch and roll rates associated with vehicle 200. Inaddition, processing unit 110 may model the road elevation by analyzingposition and motion cues present on the road surface. Further,processing unit 110 may estimate the pitch and roll rates associatedwith vehicle 200 by tracking a set of feature points in the one or moreimages.

At step 556, processing unit 110 may perform multi-frame analysis by,for example, tracking the detected segments across consecutive imageframes and accumulating frame-by-frame data associated with detectedsegments. As processing unit 110 performs multi-frame analysis, the setof measurements constructed at step 554 may become more reliable andassociated with an increasingly higher confidence level. Thus, byperforming steps 550-556, processing unit 110 may identify road marksappearing within the set of captured images and derive lane geometryinformation. Based on the identification and the derived information,processing unit 110 may cause one or more navigational responses invehicle 200, as described in connection with FIG. 5A, above.

At step 558, processing unit 110 may consider additional sources ofinformation to further develop a safety model for vehicle 200 in thecontext of its surroundings. Processing unit 110 may use the safetymodel to define a context in which system 100 may execute autonomouscontrol of vehicle 200 in a safe manner. To develop the safety model, insome embodiments, processing unit 110 may consider the position andmotion of other vehicles, the detected road edges and barriers, and/orgeneral road shape descriptions extracted from map data (such as datafrom map database 160). By considering additional sources ofinformation, processing unit 110 may provide redundancy for detectingroad marks and lane geometry and increase the reliability of system 100.

FIG. 5D is a flowchart showing an exemplary process 500D for detectingtraffic lights in a set of images, consistent with disclosedembodiments. Processing unit 110 may execute monocular image analysismodule 402 to implement process 500D. At step 560, processing unit 110may scan the set of images and identify objects appearing at locationsin the images likely to contain traffic lights. For example, processingunit 110 may filter the identified objects to construct a set ofcandidate objects, excluding those objects unlikely to correspond totraffic lights. The filtering may be done based on various propertiesassociated with traffic lights, such as shape, dimensions, texture,position (e.g., relative to vehicle 200), and the like. Such propertiesmay be based on multiple examples of traffic lights and traffic controlsignals and stored in a database. In some embodiments, processing unit110 may perform multi-frame analysis on the set of candidate objectsreflecting possible traffic lights. For example, processing unit 110 maytrack the candidate objects across consecutive image frames, estimatethe real-world position of the candidate objects, and filter out thoseobjects that are moving (which are unlikely to be traffic lights). Insome embodiments, processing unit 110 may perform color analysis on thecandidate objects and identify the relative position of the detectedcolors appearing inside possible traffic lights.

At step 562, processing unit 110 may analyze the geometry of a junction.The analysis may be based on any combination of: (i) the number of lanesdetected on either side of vehicle 200, (ii) markings (such as arrowmarks) detected on the road, and (iii) descriptions of the junctionextracted from map data (such as data from map database 160). Processingunit 110 may conduct the analysis using information derived fromexecution of monocular analysis module 402. In addition, Processing unit110 may determine a correspondence between the traffic lights detectedat step 560 and the lanes appearing near vehicle 200.

As vehicle 200 approaches the junction, at step 564, processing unit 110may update the confidence level associated with the analyzed junctiongeometry and the detected traffic lights. For instance, the number oftraffic lights estimated to appear at the junction as compared with thenumber actually appearing at the junction may impact the confidencelevel. Thus, based on the confidence level, processing unit 110 maydelegate control to the driver of vehicle 200 in order to improve safetyconditions. By performing steps 560-564, processing unit 110 mayidentify traffic lights appearing within the set of captured images andanalyze junction geometry information. Based on the identification andthe analysis, processing unit 110 may cause one or more navigationalresponses in vehicle 200, as described in connection with FIG. 5A,above.

FIG. 5E is a flowchart showing an exemplary process 500E for causing oneor more navigational responses in vehicle 200 based on a vehicle path,consistent with the disclosed embodiments. At step 570, processing unit110 may construct an initial vehicle path associated with vehicle 200.The vehicle path may be represented using a set of points expressed incoordinates (x, z), and the distance d_(i) between two points in the setof points may fall in the range of 1 to 5 meters. In one embodiment,processing unit 110 may construct the initial vehicle path using twopolynomials, such as left and right road polynomials. Processing unit110 may calculate the geometric midpoint between the two polynomials andoffset each point included in the resultant vehicle path by apredetermined offset (e.g., a smart lane offset), if any (an offset ofzero may correspond to travel in the middle of a lane). The offset maybe in a direction perpendicular to a segment between any two points inthe vehicle path. In another embodiment, processing unit 110 may use onepolynomial and an estimated lane width to offset each point of thevehicle path by half the estimated lane width plus a predeterminedoffset (e.g., a smart lane offset).

At step 572, processing unit 110 may update the vehicle path constructedat step 570. Processing unit 110 may reconstruct the vehicle pathconstructed at step 570 using a higher resolution, such that thedistance d_(k) between two points in the set of points representing thevehicle path is less than the distance d_(i) described above. Forexample, the distance d_(k) may fall in the range of 0.1 to 0.3 meters.Processing unit 110 may reconstruct the vehicle path using a parabolicspline algorithm, which may yield a cumulative distance vector Scorresponding to the total length of the vehicle path (i.e., based onthe set of points representing the vehicle path).

At step 574, processing unit 110 may determine a look-ahead point(expressed in coordinates as (x_(l), z_(l))) based on the updatedvehicle path constructed at step 572. Processing unit 110 may extractthe look-ahead point from the cumulative distance vector S, and thelook-ahead point may be associated with a look-ahead distance andlook-ahead time. The look-ahead distance, which may have a lower boundranging from 10 to 20 meters, may be calculated as the product of thespeed of vehicle 200 and the look-ahead time. For example, as the speedof vehicle 200 decreases, the look-ahead distance may also decrease(e.g., until it reaches the lower bound). The look-ahead time, which mayrange from 0.5 to 1.5 seconds, may be inversely proportional to the gainof one or more control loops associated with causing a navigationalresponse in vehicle 200, such as the heading error tracking controlloop. For example, the gain of the heading error tracking control loopmay depend on the bandwidth of a yaw rate loop, a steering actuatorloop, car lateral dynamics, and the like. Thus, the higher the gain ofthe heading error tracking control loop, the lower the look-ahead time.

At step 576, processing unit 110 may determine a heading error and yawrate command based on the look-ahead point determined at step 574.Processing unit 110 may determine the heading error by calculating thearctangent of the look-ahead point, e.g., arctan (x_(l)/z_(l)).Processing unit 110 may determine the yaw rate command as the product ofthe heading error and a high-level control gain. The high-level controlgain may be equal to: (2/look-ahead time), if the look-ahead distance isnot at the lower bound. Otherwise, the high-level control gain may beequal to: (2*speed of vehicle 200/look-ahead distance).

FIG. 5F is a flowchart showing an exemplary process 500F for determiningwhether a leading vehicle is changing lanes, consistent with thedisclosed embodiments. At step 580, processing unit 110 may determinenavigation information associated with a leading vehicle (e.g., avehicle traveling ahead of vehicle 200). For example, processing unit110 may determine the position, velocity (e.g., direction and speed),and/or acceleration of the leading vehicle, using the techniquesdescribed in connection with FIGS. 5A and 5B, above. Processing unit 110may also determine one or more road polynomials, a look-ahead point(associated with vehicle 200), and/or a snail trail (e.g., a set ofpoints describing a path taken by the leading vehicle), using thetechniques described in connection with FIG. 5E, above.

At step 582, processing unit 110 may analyze the navigation informationdetermined at step 580. In one embodiment, processing unit 110 maycalculate the distance between a snail trail and a road polynomial(e.g., along the trail). If the variance of this distance along thetrail exceeds a predetermined threshold (for example, 0.1 to 0.2 meterson a straight road, 0.3 to 0.4 meters on a moderately curvy road, and0.5 to 0.6 meters on a road with sharp curves), processing unit 110 maydetermine that the leading vehicle is likely changing lanes. In the casewhere multiple vehicles are detected traveling ahead of vehicle 200,processing unit 110 may compare the snail trails associated with eachvehicle. Based on the comparison, processing unit 110 may determine thata vehicle whose snail trail does not match with the snail trails of theother vehicles is likely changing lanes. Processing unit 110 mayadditionally compare the curvature of the snail trail (associated withthe leading vehicle) with the expected curvature of the road segment inwhich the leading vehicle is traveling. The expected curvature may beextracted from map data (e.g., data from map database 160), from roadpolynomials, from other vehicles' snail trails, from prior knowledgeabout the road, and the like. If the difference in curvature of thesnail trail and the expected curvature of the road segment exceeds apredetermined threshold, processing unit 110 may determine that theleading vehicle is likely changing lanes.

In another embodiment, processing unit 110 may compare the leadingvehicle's instantaneous position with the look-ahead point (associatedwith vehicle 200) over a specific period of time (e.g., 0.5 to 1.5seconds). If the distance between the leading vehicle's instantaneousposition and the look-ahead point varies during the specific period oftime, and the cumulative sum of variation exceeds a predeterminedthreshold (for example, 0.3 to 0.4 meters on a straight road, 0.7 to 0.8meters on a moderately curvy road, and 1.3 to 1.7 meters on a road withsharp curves), processing unit 110 may determine that the leadingvehicle is likely changing lanes. In another embodiment, processing unit110 may analyze the geometry of the snail trail by comparing the lateraldistance traveled along the trail with the expected curvature of thesnail trail. The expected radius of curvature may be determinedaccording to the calculation: (δ_(z) ²+δ_(x) ²)/2/(δ_(x)), where δ_(x)represents the lateral distance traveled and δ_(z) represents thelongitudinal distance traveled. If the difference between the lateraldistance traveled and the expected curvature exceeds a predeterminedthreshold (e.g., 500 to 700 meters), processing unit 110 may determinethat the leading vehicle is likely changing lanes. In anotherembodiment, processing unit 110 may analyze the position of the leadingvehicle. If the position of the leading vehicle obscures a roadpolynomial (e.g., the leading vehicle is overlaid on top of the roadpolynomial), then processing unit 110 may determine that the leadingvehicle is likely changing lanes. In the case where the position of theleading vehicle is such that, another vehicle is detected ahead of theleading vehicle and the snail trails of the two vehicles are notparallel, processing unit 110 may determine that the (closer) leadingvehicle is likely changing lanes.

At step 584, processing unit 110 may determine whether or not leadingvehicle 200 is changing lanes based on the analysis performed at step582. For example, processing unit 110 may make the determination basedon a weighted average of the individual analyses performed at step 582.Under such a scheme, for example, a decision by processing unit 110 thatthe leading vehicle is likely changing lanes based on a particular typeof analysis may be assigned a value of “1” (and “0” to represent adetermination that the leading vehicle is not likely changing lanes).Different analyses performed at step 582 may be assigned differentweights, and the disclosed embodiments are not limited to any particularcombination of analyses and weights. Furthermore, in some embodiments,the analysis may make use of trained system (e.g., a machine learning ordeep learning system), which may, for example, estimate a future pathahead of a current location of a vehicle based on an image captured atthe current location.

FIG. 6 is a flowchart showing an exemplary process 600 for causing oneor more navigational responses based on stereo image analysis,consistent with disclosed embodiments. At step 610, processing unit 110may receive a first and second plurality of images via data interface128. For example, cameras included in image acquisition unit 120 (suchas image capture devices 122 and 124 having fields of view 202 and 204)may capture a first and second plurality of images of an area forward ofvehicle 200 and transmit them over a digital connection (e.g., USB,wireless, Bluetooth, etc.) to processing unit 110. In some embodiments,processing unit 110 may receive the first and second plurality of imagesvia two or more data interfaces. The disclosed embodiments are notlimited to any particular data interface configurations or protocols.

At step 620, processing unit 110 may execute stereo image analysismodule 404 to perform stereo image analysis of the first and secondplurality of images to create a 3D map of the road in front of thevehicle and detect features within the images, such as lane markings,vehicles, pedestrians, road signs, highway exit ramps, traffic lights,road hazards, and the like. Stereo image analysis may be performed in amanner similar to the steps described in connection with FIGS. 5A-5D,above. For example, processing unit 110 may execute stereo imageanalysis module 404 to detect candidate objects (e.g., vehicles,pedestrians, road marks, traffic lights, road hazards, etc.) within thefirst and second plurality of images, filter out a subset of thecandidate objects based on various criteria, and perform multi-frameanalysis, construct measurements, and determine a confidence level forthe remaining candidate objects. In performing the steps above,processing unit 110 may consider information from both the first andsecond plurality of images, rather than information from one set ofimages alone. For example, processing unit 110 may analyze thedifferences in pixel-level data (or other data subsets from among thetwo streams of captured images) for a candidate object appearing in boththe first and second plurality of images. As another example, processingunit 110 may estimate a position and/or velocity of a candidate object(e.g., relative to vehicle 200) by observing that the object appears inone of the plurality of images but not the other or relative to otherdifferences that may exist relative to objects appearing in the twoimage streams. For example, position, velocity, and/or accelerationrelative to vehicle 200 may be determined based on trajectories,positions, movement characteristics, etc. of features associated with anobject appearing in one or both of the image streams.

At step 630, processing unit 110 may execute navigational responsemodule 408 to cause one or more navigational responses in vehicle 200based on the analysis performed at step 620 and the techniques asdescribed above in connection with FIG. 4 . Navigational responses mayinclude, for example, a turn, a lane shift, a change in acceleration, achange in velocity, braking, and the like. In some embodiments,processing unit 110 may use data derived from execution of velocity andacceleration module 406 to cause the one or more navigational responses.Additionally, multiple navigational responses may occur simultaneously,in sequence, or any combination thereof.

FIG. 7 is a flowchart showing an exemplary process 700 for causing oneor more navigational responses based on an analysis of three sets ofimages, consistent with disclosed embodiments. At step 710, processingunit 110 may receive a first, second, and third plurality of images viadata interface 128. For instance, cameras included in image acquisitionunit 120 (such as image capture devices 122, 124, and 126 having fieldsof view 202, 204, and 206) may capture a first, second, and thirdplurality of images of an area forward and/or to the side of vehicle 200and transmit them over a digital connection (e.g., USB, wireless,Bluetooth, etc.) to processing unit 110. In some embodiments, processingunit 110 may receive the first, second, and third plurality of imagesvia three or more data interfaces. For example, each of image capturedevices 122, 124, 126 may have an associated data interface forcommunicating data to processing unit 110. The disclosed embodiments arenot limited to any particular data interface configurations orprotocols.

At step 720, processing unit 110 may analyze the first, second, andthird plurality of images to detect features within the images, such aslane markings, vehicles, pedestrians, road signs, highway exit ramps,traffic lights, road hazards, and the like. The analysis may beperformed in a manner similar to the steps described in connection withFIGS. 5A-5D and 6 , above. For instance, processing unit 110 may performmonocular image analysis (e.g., via execution of monocular imageanalysis module 402 and based on the steps described in connection withFIGS. 5A-5D, above) on each of the first, second, and third plurality ofimages. Alternatively, processing unit 110 may perform stereo imageanalysis (e.g., via execution of stereo image analysis module 404 andbased on the steps described in connection with FIG. 6 , above) on thefirst and second plurality of images, the second and third plurality ofimages, and/or the first and third plurality of images. The processedinformation corresponding to the analysis of the first, second, and/orthird plurality of images may be combined. In some embodiments,processing unit 110 may perform a combination of monocular and stereoimage analyses. For example, processing unit 110 may perform monocularimage analysis (e.g., via execution of monocular image analysis module402) on the first plurality of images and stereo image analysis (e.g.,via execution of stereo image analysis module 404) on the second andthird plurality of images. The configuration of image capture devices122, 124, and 126—including their respective locations and fields ofview 202, 204, and 206—may influence the types of analyses conducted onthe first, second, and third plurality of images. The disclosedembodiments are not limited to a particular configuration of imagecapture devices 122, 124, and 126, or the types of analyses conducted onthe first, second, and third plurality of images.

In some embodiments, processing unit 110 may perform testing on system100 based on the images acquired and analyzed at steps 710 and 720. Suchtesting may provide an indicator of the overall performance of system100 for certain configurations of image capture devices 122, 124, and126. For example, processing unit 110 may determine the proportion of“false hits” (e.g., cases where system 100 incorrectly determined thepresence of a vehicle or pedestrian) and “misses.”

At step 730, processing unit 110 may cause one or more navigationalresponses in vehicle 200 based on information derived from two of thefirst, second, and third plurality of images. Selection of two of thefirst, second, and third plurality of images may depend on variousfactors, such as, for example, the number, types, and sizes of objectsdetected in each of the plurality of images. Processing unit 110 mayalso make the selection based on image quality and resolution, theeffective field of view reflected in the images, the number of capturedframes, the extent to which one or more objects of interest actuallyappear in the frames (e.g., the percentage of frames in which an objectappears, the proportion of the object that appears in each such frame,etc.), and the like.

In some embodiments, processing unit 110 may select information derivedfrom two of the first, second, and third plurality of images bydetermining the extent to which information derived from one imagesource is consistent with information derived from other image sources.For example, processing unit 110 may combine the processed informationderived from each of image capture devices 122, 124, and 126 (whether bymonocular analysis, stereo analysis, or any combination of the two) anddetermine visual indicators (e.g., lane markings, a detected vehicle andits location and/or path, a detected traffic light, etc.) that areconsistent across the images captured from each of image capture devices122, 124, and 126. Processing unit 110 may also exclude information thatis inconsistent across the captured images (e.g., a vehicle changinglanes, a lane model indicating a vehicle that is too close to vehicle200, etc.). Thus, processing unit 110 may select information derivedfrom two of the first, second, and third plurality of images based onthe determinations of consistent and inconsistent information.

Navigational responses may include, for example, a turn, a lane shift, achange in acceleration, and the like. Processing unit 110 may cause theone or more navigational responses based on the analysis performed atstep 720 and the techniques as described above in connection with FIG. 4. Processing unit 110 may also use data derived from execution ofvelocity and acceleration module 406 to cause the one or morenavigational responses. In some embodiments, processing unit 110 maycause the one or more navigational responses based on a relativeposition, relative velocity, and/or relative acceleration betweenvehicle 200 and an object detected within any of the first, second, andthird plurality of images. Multiple navigational responses may occursimultaneously, in sequence, or any combination thereof.

Reinforcement Learning and Trained Navigational Systems

The sections that follow discuss autonomous driving along with systemsand methods for accomplishing autonomous control of a vehicle, whetherthat control is fully autonomous (a self-driving vehicle) or partiallyautonomous (e.g., one or more driver assist systems or functions). Asshown in FIG. 8 , the autonomous driving task can be partitioned intothree main modules, including a sensing module 801, a driving policymodule 803, and a control module 805. In some embodiments, modules 801,803, and 805 may be stored in memory unit 140 and/or memory unit 150 ofsystem 100, or modules 801, 803, and 805 (or portions thereof) may bestored remotely from system 100 (e.g., stored in a server accessible tosystem 100 via, for example, wireless transceiver 172). Furthermore, anyof the modules (e.g., modules 801, 803, and 805) disclosed herein mayimplement techniques associated with a trained system (such as a neuralnetwork or a deep neural network) or an untrained system.

Sensing module 801, which may be implemented using processing unit 110,may handle various tasks relating to sensing of a navigational state inan environment of a host vehicle. Such tasks may rely upon input fromvarious sensors and sensing systems associated with the host vehicle.These inputs may include images or image streams from one or moreonboard cameras, GPS position information, accelerometer outputs, userfeedback, or user inputs to one or more user interface devices, radar,lidar, etc. Sensing, which may include data from cameras and/or anyother available sensors, along with map information, may be collected,analyzed, and formulated into a “sensed state,” describing informationextracted from a scene in the environment of the host vehicle. Thesensed state may include sensed information relating to target vehicles,lane markings, pedestrians, traffic lights, road geometry, lane shape,obstacles, distances to other objects/vehicles, relative velocities,relative accelerations, among any other potential sensed information.Supervised machine learning may be implemented in order to produce asensing state output based on sensed data provided to sensing module801. The output of the sensing module may represent a sensednavigational “state” of the host vehicle, which may be passed to drivingpolicy module 803.

While a sensed state may be developed based on image data received fromone or more cameras or image sensors associated with a host vehicle, asensed state for use in navigation may be developed using any suitablesensor or combination of sensors. In some embodiments, the sensed statemay be developed without reliance upon captured image data. In fact, anyof the navigational principles described herein may be applicable tosensed states developed based on captured image data as well as sensedstates developed using other non-image based sensors. The sensed statemay also be determined via sources external to the host vehicle. Forexample, a sensed state may be developed in full or in part based oninformation received from sources remote from the host vehicle (e.g.,based on sensor information, processed state information, etc. sharedfrom other vehicles, shared from a central server, or from any othersource of information relevant to a navigational state of the hostvehicle).

Driving policy module 803, which is discussed in more detail below andwhich may be implemented using processing unit 110, may implement adesired driving policy in order to decide on one or more navigationalactions for the host vehicle to take in response to the sensednavigational state. If there are no other agents (e.g., target vehiclesor pedestrians) present in the environment of the host vehicle, thesensed state input to driving policy module 803 may be handled in arelatively straightforward manner. The task becomes more complex whenthe sensed state requires negotiation with one or more other agents. Thetechnology used to generate the output of driving policy module 803 mayinclude reinforcement learning (discussed in more detail below). Theoutput of driving policy module 803 may include at least onenavigational action for the host vehicle and may include a desiredacceleration (which may translate to an updated speed for the hostvehicle), a desired yaw rate for the host vehicle, a desired trajectory,among other potential desired navigational actions.

Based on the output from the driving policy module 803, control module805, which may also be implemented using processing unit 110, maydevelop control instructions for one or more actuators or controlleddevices associated with the host vehicle. Such actuators and devices mayinclude an accelerator, one or more steering controls, a brake, a signaltransmitter, a display, or any other actuator or device that may becontrolled as part of a navigation operation associated with a hostvehicle. Aspects of control theory may be used to generate the output ofcontrol module 805. Control module 805 may be responsible for developingand outputting instructions to controllable components of the hostvehicle in order to implement the desired navigational goals orrequirements of driving policy module 803.

Returning to driving policy module 803, in some embodiments, a trainedsystem trained through reinforcement learning may be used to implementdriving policy module 803. In other embodiments, driving policy module803 may be implemented without a machine learning approach, by usingspecified algorithms to “manually” address the various scenarios thatmay arise during autonomous navigation. Such an approach, however, whileviable, may result in a driving policy that is too simplistic and maylack the flexibility of a trained system based on machine learning. Atrained system, for example, may be better equipped to handle complexnavigational states and may better determine whether a taxi is parkingor is stopping to pick up or drop off a passenger, determine whether apedestrian intends to cross the street ahead of the host vehicle;balance unexpected behavior of other drivers with defensiveness;negotiate in dense traffic involving target vehicles and/or pedestrians;decide when to suspend certain navigational rules or augment otherrules; anticipate unsensed, but anticipated conditions (e.g., whether apedestrian will emerge from behind a car or obstacle); etc. A trainedsystem based on reinforcement learning may also be better equipped toaddress a state space that is continuous and high-dimensional along withan action space that is continuous.

Training of the system using reinforcement learning may involve learninga driving policy in order to map from sensed states to navigationalactions. A driving policy is a function π: S→A, where S is a set ofstates and A⊂

² is the action space (e.g., desired speed, acceleration, yaw commands,etc.). The state space is S=S_(s)×S_(p), where S_(s) is the sensingstate and S_(p) is additional information on the state saved by thepolicy. Working in discrete time intervals, at time t, the current states_(t)∈S may be observed, and the policy may be applied to obtain adesired action, a_(t)=π(s_(t)).

The system may be trained through exposure to various navigationalstates, having the system apply the policy, providing a reward (based ona reward function designed to reward desirable navigational behavior).Based on the reward feedback, the system may “learn” the policy andbecomes trained in producing desirable navigational actions. Forexample, the learning system may observe the current state s_(t)∈S anddecide on an action a_(t)∈A based on a policy π:S→

(A). Based on the decided action (and implementation of the action), theenvironment moves to the next state s_(t+1)∈S for observation by thelearning system. For each action developed in response to the observedstate, the feedback to the learning system is a reward signal r₁, r₂, .. . .

The goal of Reinforcement Learning (RL) is to find a policy π. It isusually assumed that at time t, there is a reward function r_(t) whichmeasures the instantaneous quality of being at state s_(t) and takingaction a_(t). However, taking the action a_(t) at time t affects theenvironment and therefore affects the value of the future states. As aresult, when deciding on what action to take, not only should thecurrent reward be taken into account, but future rewards should also beconsidered. In some instances the system should take a certain action,even though it is associated with a reward lower than another availableoption, when the system determines that in the future a greater rewardmay be realized if the lower reward option is taken now. To formalizethis, observe that a policy, π, and an initial state, s, induces adistribution over

^(T), where the probability of a vector (r₁, . . . , r_(T)) is theprobability of observing the rewards r₁, . . . , r_(T), if the agentstarts at state s₀=s and from there on follows the policy π. The valueof the initial state s may be defined as:

${V^{\pi}(s)} = {{{\mathbb{E}}\lbrack {{ {\sum\limits_{t = 1}^{T}r_{t}} \middle| s_{0}  = s},{\forall{t \geq 1}},{a_{t} = {\pi( s_{t} )}}} \rbrack}.}$

Instead of restricting the time horizon to T, the future rewards may bediscounted to define, for some fixed γ∈(0, 1):

${V^{\pi}(s)} = {{{\mathbb{E}}\lbrack {{ {\sum\limits_{t = 1}^{\infty}{\gamma^{t}r_{t}}} \middle| s_{0}  = s},{\forall{t \geq 1}},{a_{t} = {\pi( s_{t} )}}} \rbrack}.}$

In any case, the optimal policy is the solution of

$\underset{\pi}{argmax}\;{{\mathbb{E}}\lbrack {V^{\pi}(s)} \rbrack}$

where the expectation is over the initial state, s.

There are several possible methodologies for training the driving policysystem. For example, an imitation approach (e.g., behavior cloning) maybe used in which the system learns from state/action pairs where theactions are those that would be chosen by a good agent (e.g., a human)in response to a particular observed state. Suppose a human driver isobserved. Through this observation, many examples of the form (s_(t),a_(t)), where s_(t) is the state and a_(t) is the action of the humandriver could be obtained, observed, and used as a basis for training thedriving policy system. For example, supervised learning can be used tolearn a policy π such that π(s_(t))≈a_(t). There are many potentialadvantages of this approach. First, there is no requirement to define areward function. Second, the learning is supervised and happens offline(there is no need to apply the agent in the learning process). Adisadvantage of this method is that different human drivers, and eventhe same human drivers, are not deterministic in their policy choices.Hence, learning a function for which ∥π(s_(t))−a_(t)∥ is very small isoften infeasible. And, even small errors may accumulate over time toyield large errors.

Another technique that may be employed is policy based learning. Here,the policy may be expressed in parametric form and directly optimizedusing a suitable optimization technique (e.g., stochastic gradientdescent). The approach is to directly solve the problem given in

$\underset{\pi}{argmax}\;{{{\mathbb{E}}\lbrack {V^{\pi}(s)} \rbrack}.}$There are of course many ways to solve the problem. One advantage ofthis approach is that it tackles the problem directly, and thereforeoften leads to good practical results. One potential disadvantage isthat it often requires an “on-policy” training, namely, the learning ofπ is an iterative process, where at iteration j we have a non-perfectpolicy, π_(j), and to construct the next policy π_(j), we must interactwith the environment while acting based on π_(j).

The system may also be trained through value based learning (learning Qor V functions). Suppose a good approximation can be learned to theoptimal value function V*. An optimal policy may be constructed (e.g.,by relying on the Bellman equation). Some versions of value basedlearning can be implemented offline (called “off-policy” training). Somedisadvantages of the value-based approach may result from its strongdependence on Markovian assumptions and required approximation of acomplicated function (it may be more difficult to approximate the valuefunction than to approximate the policy directly).

Another technique may include model based learning and planning(learning the probability of state transitions and solving theoptimization problem of finding the optimal V). Combinations of thesetechniques may also be used to train the learning system. In thisapproach, the dynamics of the process may be learned, namely, thefunction that takes (s_(t), a_(t)) and yields a distribution over thenext state s_(t+1). Once this function is learned, the optimizationproblem may be solved to find the policy π whose value is optimal. Thisis called “planning”. One advantage of this approach may be that thelearning part is supervised and can be applied offline by observingtriplets (s_(t), a_(t), s_(t+1)). One disadvantage of this approach,similar to the “imitation” approach, may be that small errors in thelearning process can accumulate and to yield inadequately performingpolicies.

Another approach for training driving policy module 803 may includedecomposing the driving policy function into semantically meaningfulcomponents. This allows implementation of parts of the policy manually,which may ensure the safety of the policy, and implementation of otherparts of the policy using reinforcement learning techniques, which mayenable adaptivity to many scenarios, a human-like balance betweendefensive/aggressive behavior, and a human-like negotiation with otherdrivers. From the technical perspective, a reinforcement learningapproach may combine several methodologies and offer a tractabletraining procedure, where most of the training can be performed usingeither recorded data or a self-constructed simulator.

In some embodiments, training of driving policy module 803 may rely uponan “options” mechanism. To illustrate, consider a simple scenario of adriving policy for a two-lane highway. In a direct RL approach, a policyπ that maps the state into A⊂

², where the first component of π(s) is the desired acceleration commandand the second component of π(s) is the yaw rate. In a modifiedapproach, the following policies can be constructed:

Automatic Cruise Control (ACC) policy, o_(ACC): S→A: this policy alwaysoutputs a yaw rate of 0 and only changes the speed so as to implementsmooth and accident-free driving.

ACC+Left policy, O_(L): S→A: the longitudinal command of this policy isthe same as the ACC command. The yaw rate is a straightforwardimplementation of centering the vehicle toward the middle of the leftlane, while ensuring a safe lateral movement (e.g., don't move left ifthere's a car on the left side).

ACC+Right policy, o_(R):S→A: Same as o_(L), but the vehicle may becentered toward the middle of the right lane.

These policies may be referred to as “options”. Relying on these“options”, a policy can be learned that selects options, π_(o): S→O,where O is the set of available options. In one case, O={o_(ACC), o_(L),o_(R)}. The option-selector policy, π_(o), defines an actual policy, π:S→A, by setting, for every s, π(s)=o_(π) _(o) _((s))(s).

In practice, the policy function may be decomposed into an options graph901, as shown in FIG. 9 . Another example options graph 1000 is shown inFIG. 10 . The options graph can represent a hierarchical set ofdecisions organized as a Directed Acyclic Graph (DAG). There is aspecial node called the root node 903 of the graph. This node has noincoming nodes. The decision process traverses through the graph,starting from the root node, until it reaches a “leaf” node, whichrefers to a node that has no outgoing decision lines. As shown in FIG. 9, leaf nodes may include nodes 905, 907, and 909, for example. Uponencountering a leaf node, driving policy module 803 may output theacceleration and steering commands associated with a desirednavigational action associated with the leaf node.

Internal nodes, such as nodes 911, 913, and 915, for example, may resultin implementation of a policy that chooses a child among its availableoptions. The set of available children of an internal node include allof the nodes associated with a particular internal node via decisionlines. For example, internal node 913 designated as “Merge” in FIG. 9includes three children nodes 909, 915, and 917 (“Stay,” “OvertakeRight,” and “Overtake Left,” respectively) each joined to node 913 by adecision line.

Flexibility of the decision making system may be gained by enablingnodes to adjust their position in the hierarchy of the options graph.For example, any of the nodes may be allowed to declare themselves as“critical.” Each node may implement a function “is critical,” thatoutputs “True” if the node is in a critical section of its policyimplementation. For example, a node that is responsible for a take-over,may declare itself as critical while in the middle of a maneuver. Thismay impose constraints on the set of available children of a node u,which may include all nodes v which are children of node u and for whichthere exists a path from v to a leaf node that goes through all nodesdesignated as critical. Such an approach may allow, on one hand,declaration of the desired path on the graph at each time step, while onthe other hand, stability of a policy may be preserved, especially whilecritical portions of the policy are being implemented.

By defining an options graph, the problem of learning the driving policyπ: S→A may be decomposed into a problem of defining a policy for eachnode of the graph, where the policy at internal nodes should choose fromamong available children nodes. For some of the nodes, the respectivepolicy may be implemented manually (e.g., through if-then typealgorithms specifying a set of actions in response to an observed state)while for others the policies may be implemented using a trained systembuilt through reinforcement learning. The choice between manual ortrained/learned approaches may depend on safety aspects associated withthe task and on its relative simplicity. The option graphs may beconstructed in a manner such that some of the nodes are straightforwardto implement, while other nodes may rely on trained models. Such anapproach can ensure safe operation of the system.

The following discussion provides further details regarding the role ofthe options graph of FIG. 9 within driving policy module 803. Asdiscussed above, the input to the driving policy module is a “sensedstate,” which summarizes the environment map, for example, as obtainedfrom available sensors. The output of driving policy module 803 is a setof desires (optionally, together with a set of hard constraints) thatdefine a trajectory as a solution of an optimization problem.

As described above, the options graph represents a hierarchical set ofdecisions organized as a DAG. There is a special node called the “root”of the graph. The root node is the only node that has no incoming edges(e.g., decision lines). The decision process traverses the graph,starting from the root node, until it reaches a “leaf” node, namely, anode that has no outgoing edges. Each internal node should implement apolicy that picks a child among its available children. Every leaf nodeshould implement a policy that, based on the entire path from the rootto the leaf, defines a set of Desires (e.g., a set of navigational goalsfor the host vehicle). The set of Desires, together with a set of hardconstraints that are defined directly based on the sensed state,establish an optimization problem whose solution is the trajectory forthe vehicle. The hard constraints may be employed to further increasethe safety of the system, and the Desires can be used to provide drivingcomfort and human-like driving behavior of the system. The trajectoryprovided as a solution to the optimization problem, in turn, defines thecommands that should be provided to the steering, braking, and/or engineactuators in order to accomplish the trajectory.

Returning to FIG. 9 , options graph 901 represents an options graph fora two-lane highway, including with merging lanes (meaning that at somepoints, a third lane is merged into either the right or the left lane ofthe highway). The root node 903 first decides if the host vehicle is ina plain road scenario or approaching a merge scenario. This is anexample of a decision that can be implemented based on the sensingstate. Plain road node 911 includes three child nodes: stay node 909,overtake left node 917, and overtake right node 915. Stay refers to asituation in which the host vehicle would like to keep driving in thesame lane. The stay node is a leaf node (no outgoing edges/lines).Therefore, it the stay node defines a set of Desires. The first Desireit defines may include the desired lateral position—e.g., as close aspossible to the center of the current lane of travel. There may also bea desire to navigate smoothly (e.g., within predefined or allowableacceleration maximums). The stay node may also define how the hostvehicle is to react to other vehicles. For example, the stay node mayreview sensed target vehicles and assign each a semantic meaning, whichcan be translated into components of the trajectory.

Various semantic meanings may be assigned to target vehicles in anenvironment of the host vehicle. For example, in some embodiments thesemantic meaning may include any of the following designations: 1) notrelevant: indicating that the sensed vehicle in the scene is currentlynot relevant; 2) next lane: indicating that the sensed vehicle is in anadjacent lane and an appropriate offset should be maintained relative tothis vehicle (the exact offset may be calculated in the optimizationproblem that constructs the trajectory given the Desires and hardconstraints, and can potentially be vehicle dependent—the stay leaf ofthe options graph sets the target vehicle's semantic type, which definesthe Desire relative to the target vehicle); 3) give way: the hostvehicle will attempt to give way to the sensed target vehicle by, forexample, reducing speed (especially where the host vehicle determinesthat the target vehicle is likely to cut into the lane of the hostvehicle); 4) take way: the host vehicle will attempt to take the rightof way by, for example, increasing speed; 5) follow: the host vehicledesires to maintain smooth driving following after this target vehicle;6) takeover left/right: this means the host vehicle would like toinitiate a lane change to the left or right lane. Overtake left node 917and overtake right node 915 are internal nodes that do not yet defineDesires.

The next node in options graph 901 is the select gap node 919. This nodemay be responsible for selecting a gap between two target vehicles in aparticular target lane that host vehicle desires to enter. By choosing anode of the form IDj, for some value of j, the host vehicle arrives at aleaf that designates a Desire for the trajectory optimizationproblem—e.g., the host vehicle wishes to make a maneuver so as to arriveat the selected gap. Such a maneuver may involve firstaccelerating/braking in the current lane and then heading to the targetlane at an appropriate time to enter the selected gap. If the select gapnode 919 cannot find an appropriate gap, it moves to the abort node 921,which defines a desire to move back to the center of the current laneand cancel the takeover.

Returning to merge node 913, when the host vehicle approaches a merge,it has several options that may depend on a particular situation. Forexample, as shown in FIG. 11A, host vehicle 1105 is traveling along atwo-lane road with no other target vehicles detected, either in theprimary lanes of the two-lane road or in the merge lane 1111. In thissituation, driving policy module 803, upon reaching merge node 913, mayselect stay node 909. That is, staying within its current lane may bedesired where no target vehicles are sensed as merging onto the roadway.

In FIG. 11B, the situation is slightly different. Here, host vehicle1105 senses one or more target vehicles 1107 entering the main roadway1112 from merge lane 1111. In this situation, once driving policy module803 encounters merge node 913, it may choose to initiate an overtakeleft maneuver in order to avoid the merging situation.

In FIG. 11C, host vehicle 1105 encounters one or more target vehicles1107 entering main roadway 1112 from merge lane 1111. Host vehicle 1105also detects target vehicles 1109 traveling in a lane adjacent to thelane of the host vehicle. The host vehicle also detects one or moretarget vehicles 1110 traveling in the same lane as host vehicle 1105. Inthis situation, driving policy module 803 may decide to adjust the speedof host vehicle 1105 to give way to target vehicle 1107 and to proceedahead of target vehicle 1115. This can be accomplished, for example, byprogressing to select gap node 919, which, in turn, will select a gapbetween ID0 (vehicle 1107) and ID1 (vehicle 1115) as the appropriatemerging gap. In such a case, the appropriate gap of the mergingsituation defines the objective for a trajectory planner optimizationproblem.

As discussed above, nodes of the options graph may declare themselves as“critical,” which may ensure that the selected option passes through thecritical nodes. Formally, each node may implement a function IsCritical.After performing a forward pass on the options graph, from the root to aleaf, and solving the optimization problem of the trajectory planner, abackward pass may be performed from the leaf back to the root. Alongthis backward pass, the IsCritical function of all nodes in the pass maybe called, and a list of all critical nodes may be saved. In the forwardpath corresponding to the next time frame, driving policy module 803 maybe required to choose a path from the root node to a leaf that goesthrough all critical nodes.

FIGS. 11A-11C may be used to show a potential benefit of this approach.For example, in a situation where an overtake action is initiated, anddriving policy module 803 arrives at the leaf corresponding to IDk, itwould be undesirable to choose, for example, the stay node 909 when thehost vehicle is in the middle of the takeover maneuver. To avoid suchjumpiness, the IDJ node can designate itself as critical. During themaneuver, the success of the trajectory planner can be monitored, andfunction IsCritical will return a “True” value if the overtake maneuverprogresses as intended. This approach may ensure that in the next timeframe, the takeover maneuver will be continued (rather than jumping toanother, potentially inconsistent maneuver prior to completion of theinitially selected maneuver). If, on the other hand, monitoring of themaneuver indicates that the selected maneuver is not progressing asintended, or if the maneuver has become unnecessary or impossible, thefunction IsCritical can return a “False” value. This can allow theselect gap node to select a different gap in the next time frame, or toabort the overtake maneuver altogether. This approach may allow, on onehand, declaration of the desired path on the options graph at each timestep, while on the other hand, may help to promote stability of thepolicy while in critical parts of the execution.

Hard constraints, which will be discussed in more detail below, may bedifferentiated from navigational desires. For example, hard constraintsmay ensure safe driving by applying an added layer of filtering of aplanned navigational action. The implicated hard constraints, which maybe programmed and defined manually, rather than through use of a trainedsystem built upon reinforcement learning, can be determined from thesensed state. In some embodiments, however, the trained system may learnthe applicable hard constraints to be applied and followed. Such anapproach may promote driving policy module 803 arriving at a selectedaction that is already in compliance with the applicable hardconstraints, which may reduce or eliminate selected actions that mayrequire later modification to comply with applicable hard constraints.Nevertheless, as a redundant safety measure, hard constraints may beapplied to the output of driving policy module 803 even where drivingpolicy module 803 has been trained to account for predetermined hardconstraints.

There are many examples of potential hard constraints. For example, ahard constraint may be defined in conjunction with a guardrail on anedge of a road. In no situation may the host vehicle be allowed to passthe guardrail. Such a rule induces a hard lateral constraint on thetrajectory of the host vehicle. Another example of a hard constraint mayinclude a road bump (e.g., a speed control bump), which may induce ahard constraint on the speed of driving before the bump and whiletraversing the bump. Hard constraints may be considered safety criticaland, therefore, may be defined manually rather than relying solely on atrained system learning the constraints during training.

In contrast to hard constraints, the goal of desires may be to enable orachieve comfortable driving. As discussed above, an example of a desiremay include a goal of positioning the host vehicle at a lateral positionwithin a lane that corresponds to the center of the host vehicle lane.Another desire may include the ID of a gap to fit into. Note that thereis not a requirement for the host vehicle to be exactly in the center ofthe lane, but instead a desire to be as close as possible to it mayensure that the host vehicle tends to migrate to the center of the laneeven in the event of deviations from the center of the lane. Desires maynot be safety critical. In some embodiments, desires may requirenegotiation with other drivers and pedestrians. One approach forconstructing the desires may rely on the options graph, and the policyimplemented in at least some nodes of the graph may be based onreinforcement learning.

For the nodes of options graph 901 or 1000 implemented as nodes trainedbased on learning, the training process may include decomposing theproblem into a supervised learning phase and a reinforcement learningphase. In the supervised learning phase, a differentiable mapping from(s_(t), a_(t)) to ŝ_(t+1) can be learned such that ŝ_(t+1)≈s_(t+1). Thismay be similar to “model-based” reinforcement learning. However, in theforward loop of the network, ŝ_(t+1) may be replaced by the actual valueof s_(t+1), therefore eliminating the problem of error accumulation. Therole of prediction of ŝ_(t+1) is to propagate messages from the futureback to past actions. In this sense, the algorithm may be a combinationof “model-based” reinforcement learning with “policy-based learning.”

An important element that may be provided in some scenarios is adifferentiable path from future losses/rewards back to decisions onactions. With the option graph structure, the implementation of optionsthat involve safety constraints are usually not differentiable. Toovercome this issue, the choice of a child in a learned policy node maybe stochastic. That is, a node may output a probability vector, p, thatassigns probabilities used in choosing each of the children of theparticular node. Suppose that a node has k children and let a⁽¹⁾, . . ., a^((k)) be the actions of the path from each child to a leaf. Theresulting predicted action is therefore â=Σ_(i=1) ^(k)p_(i)a^((i)),which may result in a differentiable path from the action to p. Inpractice, an action a may be chosen to be a^((i)) for i˜p, and thedifference between a and â may be referred to as additive noise.

For the training of ŝ_(t+1) given s_(t), a_(t), supervised learning maybe used together with real data. For training the policy of nodessimulators can be used. Later, fine tuning of a policy can beaccomplished using real data. Two concepts may make the simulation morerealistic. First, using imitation, an initial policy can be constructedusing the “behavior cloning” paradigm, using large real world data sets.In some cases, the resulting agents may be suitable. In other cases, theresulting agents at least form very good initial policies for the otheragents on the roads. Second, using self-play, our own policy may be usedto augment the training. For example, given an initial implementation ofthe other agents (cars/pedestrians) that may be experienced, a policymay be trained based on a simulator. Some of the other agents may bereplaced with the new policy, and the process may be repeated. As aresult, the policy can continue to improve as it should respond to alarger variety of other agents that have differing levels ofsophistication.

Further, in some embodiments, the system may implement a multi-agentapproach. For example, the system may take into account data fromvarious sources and/or images capturing from multiple angles. Further,some disclosed embodiments may provide economy of energy, asanticipation of an event which does not directly involve the hostvehicle, but which may have an effect on the host vehicle can beconsidered, or even anticipation of an event that may lead tounpredictable circumstances involving other vehicles may be aconsideration (e.g., radar may “see through” the leading vehicle andanticipation of an unavoidable, or even a high likelihood of an eventthat will affect the host vehicle).

Trained System with Imposed Navigational Constraints

In the context of autonomous driving, a significant concern is how toensure that a learned policy of a trained navigational network will besafe. In some embodiments, the driving policy system may be trainedusing constraints, such that the actions selected by the trained systemmay already account for applicable safety constraints. Additionally, insome embodiments, an extra layer of safety may be provided by passingthe selected actions of the trained system through one or more hardconstraints implicated by a particular sensed scene in the environmentof the host vehicle. Such an approach may ensure that that the actionstaken by the host vehicle have been restricted to those confirmed assatisfying applicable safety constraints.

At its core, the navigational system may include a learning algorithmbased on a policy function that maps an observed state to one or moredesired actions. In some implementations, the learning algorithm is adeep learning algorithm. The desired actions may include at least oneaction expected to maximize an anticipated reward for a vehicle. Whilein some cases, the actual action taken by the vehicle may correspond toone of the desired actions, in other cases, the actual action taken maybe determined based on the observed state, one or more desired actions,and non-learned, hard constraints (e.g., safety constraints) imposed onthe learning navigational engine. These constraints may include no-drivezones surrounding various types of detected objects (e.g., targetvehicles, pedestrians, stationary objects on the side of a road or in aroadway, moving objects on the side of a road or in a roadway, guardrails, etc.) In some cases, the size of the zone may vary based on adetected motion (e.g., speed and/or direction) of a detected object.Other constraints may include a maximum speed of travel when passingwithin an influence zone of a pedestrian, a maximum deceleration (toaccount for a target vehicle spacing behind the host vehicle), amandatory stop at a sensed crosswalk or railroad crossing, etc.

Hard constraints used in conjunction with a system trained throughmachine learning may offer a degree of safety in autonomous driving thatmay surpass a degree of safety available based on the output of thetrained system alone. For example, the machine learning system may betrained using a desired set of constraints as training guidelines and,therefore, the trained system may select an action in response to asensed navigational state that accounts for and adheres to thelimitations of applicable navigational constraints. Still, however, thetrained system has some flexibility in selecting navigational actionsand, therefore, there may exist at least some situations in which anaction selected by the trained system may not strictly adhere torelevant navigational constraints. Therefore, in order to require that aselected action strictly adheres to relevant navigational constraints,the output of the trained system may be combined with, compared to,filtered with, adjusted, modified, etc. using a non-machine learningcomponent outside the learning/trained framework that guarantees strictapplication of relevant navigational constraints.

The following discussion provides additional details regarding thetrained system and the potential benefits (especially from a safetyperspective) that may be gleaned from combining a trained system with analgorithmic component outside of the trained/learning framework. Asdiscussed, the reinforcement learning objective by policy may beoptimized through stochastic gradient ascent. The objective (e.g., theexpected reward) may be defined as

_(E˜P) ₀ R(s).

.

Objectives that involve expectation may be used in machine learningscenarios. Such an objective, without being bound by navigationalconstraints, however, may not return actions strictly bound by thoseconstraints. For example, considering a reward function for whichR(s)=−r for trajectories that represent a rare “corner” event to beavoided (e.g., such as an accident), and R(s)∈[−1, 1] for the rest ofthe trajectories, one goal for the learning system may be to learn toperform an overtake maneuver. Normally, in an accident free trajectory,R(s) would reward successful, smooth, takeovers and penalize staying ina lane without completing the takeover-hence the range [−1, 1]. If asequence, {tilde over (s)}, represents an accident, the reward, −r,should provide a sufficiently high penalty to discourage such anoccurrence. The question is what should be the value of r to ensureaccident-free driving.

Observe that the effect of an accident on

[R(s)] is the additive term −pr where p is the probability mass oftrajectories with an accident event. If this term is negligible, i.e.,p<<1/r, then the learning system may prefer a policy that performs anaccident (or adopt in general a reckless driving policy) in order tofulfill the takeover maneuver successfully more often than a policy thatwould be more defensive at the expense of having some takeover maneuversnot complete successfully. In other words, if the probability ofaccidents is to be at most p, then r must be set such that r>>1/p. Itmay be desirable to make p extremely small (e.g., on the order ofp=10⁻⁹). Therefore, r should be large. In policy gradient, the gradientof

[R(s)] may be estimated. The following lemma shows that the variance ofthe random variable R(s) grows with pr², which is larger than r forr>>1/p. Therefore, estimating the objective may be difficult, andestimating its gradient may be even more difficult.

Lemma: Let π_(o) be a policy and let p and r be scalars such that withprobability p, R(s)=−r is obtained, and with probability 1−p we haveR(s)∈[−1, 1] is obtained. Then,Var[R( s )]≥pr ²−(pr+(1−p))²=(p−p ²)r ²−2p(1−p)r−(1−p)² ≈pr ²

where the last approximation holds for the case r≥1/p.

This discussion shows that an objection of the form

[R(s)] may not ensure functional safety without causing a varianceproblem. The baseline subtraction method for variance reduction may notoffer a sufficient remedy to the problem because the problem would shiftfrom a high variance of R(S) to an equally high variance of the baselineconstants whose estimation would equally suffer numeric instabilities.Moreover, if the probability of an accident is p, then on average atleast 1/p sequences should be sampled before obtaining an accidentevent. This implies a lower bound of 1/p samples of sequences for alearning algorithm that aims at minimizing

[R(s)]. The solution to this problem may be found in the architecturaldesign described herein, rather than through numerical conditioningtechniques. The approach here is based on the notion that hardconstraints should be injected outside of the learning framework. Inother words, the policy function may be decomposed into a learnable partand a nonlearnable part. Formally, the policy function may be structuredas π₀=π^((T))∘π₀ ^((D)), where π₀ ^((D)) maps the (agnostic) state spaceinto a set of Desires (e.g., desired navigational goals, etc.), whileπ^((T)) maps the Desires into a trajectory (which may determine how thecar should move in a short range). The function π₀ ^((D)) is responsiblefor the comfort of driving and for making strategic decisions such aswhich other cars should be over-taken or given way and what is thedesired position of the host vehicle within its lane, etc. The mappingfrom sensed navigational state to Desires is a policy π₀ ^((D)) that maybe learned from experience by maximizing an expected reward. The desiresproduced by π₀ ^((D)) may be translated into a cost function overdriving trajectories. The function π^((T)), not a learned function, maybe implemented by finding a trajectory that minimizes the cost subjectto hard constraints on functional safety. This decomposition may ensurefunctional safety while at the same time providing for comfortabledriving.

A double merge navigational situation, as depicted in FIG. 11D, providesan example further illustrating these concepts. In a double merge,vehicles approach the merge area 1130 from both left and right sides.And, from each side, a vehicle, such as vehicle 1133 or vehicle 1135,can decide whether to merge into lanes on the other side of merge area1130. Successfully executing a double merge in busy traffic may requiresignificant negotiation skills and experience and may be difficult toexecute in a heuristic or brute force approach by enumerating allpossible trajectories that could be taken by all agents in the scene. Inthis double merge example, a set of Desires,

, appropriate for the double merge maneuver may be defined.

may be the Cartesian product of the following sets:

=[0, v_(max)]×L×{g, t, o}^(n), where [0, v_(max)] is the desired targetspeed of the host vehicle, L={1, 1.5, 2, 2.5, 3, 3.5, 4} is the desiredlateral position in lane units where whole numbers designate a lanecenter and fractional numbers designate lane boundaries, and {g, t, o}are classification labels assigned to each of the n other vehicles. Theother vehicles may be assigned “g” if the host vehicle is to give way tothe other vehicle, “t” if the host vehicle is to take way relative tothe other vehicle, or “o” if the host vehicle is to maintain an offsetdistance relative to the other vehicle.

Below is a description of how a set of Desires, (v, l, c₁, . . . , c₂)∈

, may be translated into a cost function over driving trajectories. Adriving trajectory may be represented by (x₁, y₁), . . . , (x_(k),y_(k)), where (x_(i), y_(i)) is the (lateral, longitudinal) location ofthe host vehicle (in ego-centric units) at timer τ·i. In someexperiments, τ=0.1 Sec and k=10. Of course, other values may be selectedas well. The cost assigned to a trajectory may include a weighted sum ofindividual costs assigned to the desired speed, lateral position, andthe label assigned to each of the other n vehicles.

Given a desired speed v∈[0, v_(max)], the cost of a trajectoryassociated with speed isΣ_(i=2) ^(k)(v−∥(x _(i) ,y _(i))−(x _(i−1) ,y _(i−1))∥/τ)².

Given desired lateral position, l∈L, the cost associated with desiredlateral position isΣ_(i−1) ^(k)=dist(x _(i) ,y _(i) ,l)

where dist(x, y, l) is the distance from the point (x, y) to the laneposition l. Regarding the cost due to other vehicles, for any othervehicle (x₁′, y₁′), . . . , (x_(k)′, y_(k)′) may represent the othervehicle in egocentric units of the host vehicle, and i may be theearliest point for which there exists j such that the distance between(x_(i), y_(i)) and (x′_(j), y′_(j)) is small. If there is no such point,then i can be set as i=∞. If another car is classified as “give-way”, itmay be desirable that τi>τj+0.5, meaning that the host vehicle willarrive to the trajectory intersection point at least 0.5 seconds afterthe other vehicle will arrive at the same point. A possible formula fortranslating the above constraint into a cost is [τ(j−i)+0.5]₊.

Likewise, if another car is classified as “take-way”, it may bedesirable that τj>τi+0.5, which may be translated to the cost[τ(i−j)+0.5]₊. If another car is classified as “offset”, it may bedesirable that i=∞, meaning that the trajectory of the host vehicle andthe trajectory of the offset car do not intersect. This condition can betranslated to a cost by penalizing with respect to the distance betweentrajectories.

Assigning a weight to each of these costs may provide a single objectivefunction for the trajectory planner, π^((T)). A cost that encouragessmooth driving may be added to the objective. And, to ensure functionalsafety of the trajectory, hard constraints can be added to theobjective. For example, (x_(i),y_(i)) may be prohibited from being offthe roadway, and (x_(i),y_(i)) may be forbidden from being close to(x′_(j), y′_(j)) for any trajectory point (x′_(j), y′j) of any othervehicle if |i−j| is small.

To summarize, the policy, π_(θ), can be decomposed into a mapping fromthe agnostic state to a set of Desires and a mapping from the Desires toan actual trajectory. The latter mapping is not based on learning andmay be implemented by solving an optimization problem whose cost dependson the Desires and whose hard constraints may guarantee functionalsafety of the policy.

The following discussion describes mapping from the agnostic state tothe set of Desires. As described above, to be compliant with functionalsafety, a system reliant upon reinforcement learning alone may suffer ahigh and unwieldy variance on the reward R(s). This result may beavoided by decomposing the problem into a mapping from (agnostic) statespace to a set of Desires using policy gradient iterations followed by amapping to an actual trajectory which does not involve a system trainedbased on machine learning.

For various reasons, the decision making may be further decomposed intosemantically meaningful components. For example, the size of

might be large and even continuous. In the double-merge scenariodescribed above with respect to FIG. 11D,

=[0, v_(max)]×L×{g, t, o}^(n)). Additionally, the gradient estimator mayinvolve the term Σ_(t−1) ^(T)∇_(θ)π₀(a_(t)|s_(t)). In such anexpression, the variance may grow with the time horizon T. In somecases, the value of T may be roughly 250 which may be high enough tocreate significant variance. Supposing a sampling rate is in the rangeof 10 Hz and the merge area 1130 is 100 meters, preparation for themerge may begin approximately 300 meters before the merge area. If thehost vehicle travels at 16 meters per second (about 60 km per hour),then the value of T for an episode may be roughly 250.

Returning to the concept of an options graph, an options graph that maybe representative of the double merge scenario depicted in FIG. 11D isshown in FIG. 11E. As previously discussed, an options graph mayrepresent a hierarchical set of decisions organized as a DirectedAcyclic Graph (DAG). There may be a special node in the graph called the“root” node 1140, which may be the only node that has no incoming edges(e.g., decision lines). The decision process may traverse the graph,starting from the root node, until it reaches a “leaf” node, namely, anode that has no outgoing edges. Each internal node may implement apolicy function that chooses a child from among its available children.There may be a predefined mapping from the set of traversals over theoptions graph to the set of desires

. In other words, a traversal on the options graph may be automaticallytranslated into a desire in

. Given a node, v, in the graph, a parameter vector θ_(v) may specifythe policy of choosing a child of v. If θ is the concatenation of allthe θ_(v), then π_(θ) ^((D)) may be defined by traversing from the rootof the graph to a leaf, while at each node v using the policy defined byθ_(v), to choose a child node.

In the double merge options graph 1139 of FIG. 1E, root node 1140 mayfirst decide if the host vehicle is within the merging area (e.g., area1130 of FIG. 11D) or if the host vehicle instead is approaching themerging area and needs to prepare for a possible merge. In both cases,the host vehicle may need to decide whether to change lanes (e.g., tothe left or to the right side) or whether to stay in the current lane.If the host vehicle has decided to change lanes, the host vehicle mayneed to decide whether conditions are suitable to go on and perform thelane change maneuver (e.g., at “go” node 1142). If it is not possible tochange lanes, the host vehicle may attempt to “push” toward the desiredlane (e.g., at node 1144 as part of a negotiation with vehicles in thedesired lane) by aiming at being on the lane mark. Alternatively, thehost vehicle may opt to “stay” in the same lane (e.g., at node 1146).Such a process may determine the lateral position for the host vehiclein a natural way. For example,

This may enable determination of the desired lateral position in anatural way. For example, if the host vehicle changes lanes from lane 2to lane 3, the “go” node may set the desired lateral position to 3, the“stay” node may set the desired lateral position to 2, and the “push”node may set the desired lateral position to 2.5. Next, the host vehiclemay decide whether to maintain the “same” speed (node 1148),“accelerate” (node 1150), or “decelerate” (node 1152). Next, the hostvehicle may enter a “chain like” structure 1154 that goes over the othervehicles and sets their semantic meaning to a value in the set {g, t,o}. This process may set the desires relative to the other vehicles. Theparameters of all nodes in this chain may be shared (similar toRecurrent Neural Networks).

A potential benefit of the options is the interpretability of theresults. Another potential benefit is that the decomposable structure ofthe set

can be relied upon and, therefore, the policy at each node may be chosenfrom among a small number of possibilities. Additionally, the structuremay allow for a reduction in the variance of the policy gradientestimator.

As discussed above, the length of an episode in the double mergescenario may be roughly T=250 steps. Such a value (or any other suitablevalue depending on a particular navigational scenario) may provideenough time to see the consequences of the host vehicle actions (e.g.,if the host vehicle decided to change lanes as a preparation for themerge, the host vehicle will see the benefit only after a successfulcompletion of the merge). On the other hand, due to the dynamic ofdriving, the host vehicle must make decisions at a fast enough frequency(e.g., 10 Hz in the case described above).

The options graph may enable a decrease in the effective value of T inat least two ways. First, given higher level decisions, a reward can bedefined for lower level decisions while taking into account shorterepisodes. For example, when the host vehicle has already chosen a “lanechange” and the “go” node, a policy can be learned for assigningsemantic meaning to vehicles by looking at episodes of 2-3 seconds(meaning that T becomes 20-30 instead of 250). Second, for high leveldecisions (such as whether to change lanes or to stay in the same lane),the host vehicle may not need to make decisions every 0.1 seconds.Instead, the host vehicle may be able to either make decisions at alower frequency (e.g., every second), or implement an “optiontermination” function, and then the gradient may be calculated onlyafter every termination of the option. In both cases, the effectivevalue of T may be an order of magnitude smaller than its original value.All in all, the estimator at every node may depend on a value of T whichis an order of magnitude smaller than the original 250 steps, which mayimmediately transfer to a smaller variance.

As discussed above, hard constraints may promote safer driving, andthere may be several different types of constraints. For example, statichard constraints may be defined directly from the sensing state. Thesemay include speed bumps, speed limits, road curvature, junctions, etc.,within the environment of the host vehicle that may implicate one ormore constraints on vehicle speed, heading, acceleration, breaking(deceleration), etc. Static hard constraints may also include semanticfree space where the host vehicle is prohibited from going outside ofthe free space and from navigating too close to physical barriers, forexample. Static hard constraints may also limit (e.g., prohibit)maneuvers that do not comply with various aspects of a kinematic motionof the vehicle, for example, a static hard constraint can be used toprohibit maneuvers that might lead to the host vehicle overturning,sliding, or otherwise losing control.

Hard constraints may also be associated with vehicles. For example, aconstraint may be employed requiring that a vehicle maintain alongitudinal distance to other vehicles of at least one meter and alateral distance from other vehicles of at least 0.5 meters. Constraintsmay also be applied such that the host vehicle will avoid maintaining acollision course with one or more other vehicles. For example, a time τmay be a measure of time based on a particular scene. The predictedtrajectories of the host vehicle and one or more other vehicles may beconsidered from a current time to time τ. Where the two trajectoriesintersect, (t_(t) ^(a), t_(t) ^(l)) may represent the time of arrivaland the leaving time of vehicle i to the intersection point. That is,each car will arrive at point when a first part of the car passes theintersection point, and a certain amount of time will be required beforethe last part of the car passes through the intersection point. Thisamount of time separates the arrival time from the leaving time.Assuming that t₁ ^(a)<t₂ ^(a) to (i.e., that the arrival time of vehicle1 is less than the arrival time of vehicle 2), then we will want toensure that vehicle 1 has left the intersection point prior to vehicle 2arriving. Otherwise, a collision would result. Thus, a hard constraintmay be implemented such that t₁ ^(l)>t₂ ^(a). Moreover, to ensure thatvehicle 1 and vehicle 2 do not miss one another by a minimal amount, anadded margin of safety may be obtained by including a buffer time intothe constraint (e.g., 0.5 seconds or another suitable value). A hardconstraint relating to predicted intersection trajectories of twovehicles may be expressed as t₁ ^(l)>t₂ ^(a)+0.5.

The amount of time τ over which the trajectories of the host vehicle andone or more other vehicles are tracked may vary. Injunction scenarios,however, where speeds may be lower, τ may be longer, and τ may bedefined such that a host vehicle will enter and leave the junction inless than τ seconds.

Applying hard constraints to vehicle trajectories, of course, requiresthat the trajectories of those vehicles be predicted. For the hostvehicle, trajectory prediction may be relatively straightforward, as thehost vehicle generally already understands and, indeed, is planning anintended trajectory at any given time. Relative to other vehicles,predicting their trajectories can be less straightforward. For othervehicles, the baseline calculation for determining predictedtrajectories may rely on the current speed and heading of the othervehicles, as determined, for example, based on analysis of an imagestream captured by one or more cameras and/or other sensors (radar,lidar, acoustic, etc.) aboard the host vehicle.

There can be some exceptions, however, that can simplify the problem orat least provide added confidence in a trajectory predicted for anothervehicle. For example, with respect to structured roads in which there isan indication of lanes and where give-way rules may exist, thetrajectories of other vehicles can be based, at least in part, upon theposition of the other vehicles relative to the lanes and based uponapplicable give-way rules. Thus, in some situations, when there areobserved lane structures, it may be assumed that next-lane vehicles willrespect lane boundaries. That is, the host vehicle may assume that anext-lane vehicle will stay in its lane unless there is observedevidence (e.g., a signal light, strong lateral movement, movement acrossa lane boundary) indicating that the next-lane vehicle will cut into thelane of the host vehicle.

Other situations may also provide clues regarding the expectedtrajectories of other vehicles. For example, at stop signs, trafficlights, roundabouts, etc., where the host vehicle may have the right ofway, it may be assumed that other vehicles will respect that right ofway. Thus, unless there is observed evidence of a rule break, othervehicles may be assumed to proceed along a trajectory that respects therights of way possessed by the host vehicle.

Hard constraints may also be applied with respect to pedestrians in anenvironment of the host vehicle. For example, a buffer distance may beestablished with respect to pedestrians such that the host vehicle isprohibited from navigating any closer than the prescribed bufferdistance relative to any observed pedestrian. The pedestrian bufferdistance may be any suitable distance. In some embodiments, the bufferdistance may be at least one meter relative to an observed pedestrian.

Similar to the situation with vehicles, hard constraints may also beapplied with respect to relative motion between pedestrians and the hostvehicle. For example, the trajectory of a pedestrian (based on a headingdirection and speed) may be monitored relative to the projectedtrajectory of the host vehicle. Given a particular pedestriantrajectory, with every point p on the trajectory, t(p) may represent thetime required for the pedestrian to reach point p. To maintain therequired buffer distance of at least 1 meter from the pedestrian, eithert(p) must be larger than the time the host vehicle will reach point p(with sufficient difference in time such that the host vehicle passes infront of the pedestrian by a distance of at least one meter) or thatt(p) must be less than the time the host vehicle will reach point p(e.g., if the host vehicle brakes to give way to the pedestrian). Still,in the latter example, the hard constraint may require that the hostvehicle arrive at point p at a sufficient time later than the pedestriansuch that the host vehicle can pass behind the pedestrian and maintainthe required buffer distance of at least one meter. Of course, there maybe exceptions to the pedestrian hard constraint. For example, where thehost vehicle has the right of way or where speeds are very slow, andthere is no observed evidence that the pedestrian will decline to giveway to the host vehicle or will otherwise navigate toward the hostvehicle, the pedestrian hard constraint may be relaxed (e.g., to asmaller buffer of at least 0.75 meters or 0.50 meters).

In some examples, constraints may be relaxed where it is determined thatnot all can be met. For example, in situations where a road is toonarrow to leave desired spacing (e.g., 0.5 meters) from both curbs orfrom a curb and a parked vehicle, one or more the constraints may berelaxed if there are mitigating circumstances. For example, if there areno pedestrians (or other objects) on the sidewalk one can proceed slowlyat 0.1 meters from a curb. In some embodiments, constraints may berelaxed if doing so will improve the user experience. For example, inorder to avoid a pothole, constraints may be relaxed to allow a vehicleto navigate closers to the edges of the lane, a curb, or a pedestrianmore than might ordinarily be permitted. Furthermore, when determiningwhich constrains to relax, in some embodiments, the one or moreconstraints chosen to relax are those deemed to have the least availablenegative impact to safety. For example, a constraint relating to howclose the vehicle may travel to the curb or to a concrete barrier may berelaxed before relaxing one dealing with proximity to other vehicles. Insome embodiments, pedestrian constraints may be the last to be relaxed,or may never be relaxed in some situations.

FIG. 12 shows an example of a scene that may be captured and analyzedduring navigation of a host vehicle. For example, a host vehicle mayinclude a navigation system (e.g., system 100), as described above, thatmay receive from a camera (e.g., at least one of image capture device122, image capture device 124, and image capture device 126) associatedwith the host vehicle a plurality of images representative of anenvironment of the host vehicle. The scene shown in FIG. 12 is anexample of one of the images that may be captured at time t from anenvironment of a host vehicle traveling in lane 1210 along a predictedtrajectory 1212. The navigation system may include at least oneprocessing device (e.g., including any of the EyeQ processors or otherdevices described above) that are specifically programmed to receive theplurality of images and analyze the images to determine an action inresponse to the scene. Specifically, the at least one processing devicemay implement sensing module 801, driving policy module 803, and controlmodule 805, as shown in FIG. 8 . Sensing module 801 may be responsiblefor collecting and outputting the image information collected from thecameras and providing that information, in the form of an identifiednavigational state, to driving policy module 803, which may constitute atrained navigational system that has been trained through machinelearning techniques, such as supervised learning, reinforcementlearning, etc. Based on the navigational state information provided todriving policy module 803 by sensing module 801, driving policy module803 (e.g., by implementing the options graph approach described above)may generate a desired navigational action for execution by the hostvehicle in response to the identified navigational state.

In some embodiments, the at least one processing device may translatethe desired navigation action directly into navigational commands using,for example, control module 805. In other embodiments, however, hardconstraints may be applied such that the desired navigational actionprovided by the driving policy module 803 is tested against variouspredetermined navigational constraints that may be implicated by thescene and the desired navigational action. For example, where drivingpolicy module 803 outputs a desired navigational action that would causethe host vehicle to follow trajectory 1212, this navigational action maybe tested relative to one or more hard constraints associated withvarious aspects of the environment of the host vehicle. For example, acaptured image 1201 may reveal a curb 1213, a pedestrian 1215, a targetvehicle 1217, and a stationary object (e.g., an overturned box) presentin the scene. Each of these may be associated with one or more hardconstraints. For example, curb 1213 may be associated with a staticconstraint that prohibits the host vehicle from navigating into the curbor past the curb and onto a sidewalk 1214. Curb 1213 may also beassociated with a road barrier envelope that defines a distance (e.g., abuffer zone) extending away from (e.g., by 0.1 meters, 0.25 meters, 0.5meters, 1 meter, etc.) and along the curb, which defines a no-navigatezone for the host vehicle. Of course, static constraints may beassociated with other types of roadside boundaries as well (e.g., guardrails, concrete pillars, traffic cones, pylons, or any other type ofroadside barrier).

It should be noted that distances and ranging may be determined by anysuitable method. For example, in some embodiments, distance informationmay be provided by onboard radar and/or lidar systems. Alternatively oradditionally, distance information may be derived from analysis of oneor more images captured from the environment of the host vehicle. Forexample, numbers of pixels of a recognized object represented in animage may be determined and compared to known field of view and focallength geometries of the image capture devices to determine scale anddistances. Velocities and accelerations may be determined, for example,by observing changes in scale between objects from image to image overknown time intervals. This analysis may indicate the direction ofmovement toward or away from the host vehicle along with how fast theobject is pulling away from or coming toward the host vehicle. Crossingvelocity may be determined through analysis of the change in an object'sX coordinate position from one image to another over known time periods.

Pedestrian 1215 may be associated with a pedestrian envelope thatdefines a buffer zone 1216. In some cases, an imposed hard constraintmay prohibit the host vehicle from navigating within a distance of 1meter from pedestrian 1215 (in any direction relative to thepedestrian). Pedestrian 1215 may also define the location of apedestrian influence zone 1220. Such an influence zone may be associatedwith a constraint that limits the speed of the host vehicle within theinfluence zone. The influence zone may extend 5 meters, 10 meters, 20meters, etc., from pedestrian 1215. Each graduation of the influencezone may be associated with a different speed limit. For example, withina zone of 1 meter to five meters from pedestrian 1215, host vehicle maybe limited to a first speed (e.g., 10 mph, 20 mph, etc.) that may beless than a speed limit in a pedestrian influence zone extending from 5meters to 10 meters. Any graduation for the various stages of theinfluence zone may be used. In some embodiments, the first stage may benarrower than from 1 meter to five meters and may extend only from onemeter to two meters. In other embodiments, the first stage of theinfluence zone may extend from 1 meter (the boundary of the no-navigatezone around a pedestrian) to a distance of at least 10 meters. A secondstage, in turn, may extend from 10 meters to at least about 20 meters.The second stage may be associated with a maximum rate of travel for thehost vehicle that is greater than the maximum rate of travel associatedwith the first stage of the pedestrian influence zone.

One or more stationary object constraints may also be implicated by thedetected scene in the environment of the host vehicle. For example, inimage 1201, the at least one processing device may detect a stationaryobject, such as box 1219 present in the roadway. Detected stationaryobjects may include various objects, such as at least one of a tree, apole, a road sign, or an object in a roadway. One or more predefinednavigational constraints may be associated with the detected stationaryobject. For example, such constraints may include a stationary objectenvelope, wherein the stationary object envelope defines a buffer zoneabout the object within which navigation of the host vehicle may beprohibited. At least a portion of the buffer zone may extend apredetermined distance from an edge of the detected stationary object.For example, in the scene represented by image 1201, a buffer zone of atleast 0.1 meters, 0.25 meters, 0.5 meters or more may be associated withbox 1219 such that the host vehicle will pass to the right or to theleft of the box by at least some distance (e.g., the buffer zonedistance) in order to avoid a collision with the detected stationaryobject.

The predefined hard constraints may also include one or more targetvehicle constraints. For example, a target vehicle 1217 may be detectedin image 1201. To ensure that the host vehicle does not collide withtarget vehicle 1217, one or more hard constraints may be employed. Insome cases, a target vehicle envelope may be associated with a singlebuffer zone distance. For example, the buffer zone may be defined by a 1meter distance surrounding the target vehicle in all directions. Thebuffer zone may define a region extending from the target vehicle by atleast one meter into which the host vehicle is prohibited fromnavigating.

The envelope surrounding target vehicle 1217 need not be defined by afixed buffer distance, however. In some cases, the predefined hardconstraints associate with target vehicles (or any other movable objectsdetected in the environment of the host vehicle) may depend on theorientation of the host vehicle relative to the detected target vehicle.For example, in some cases, a longitudinal buffer zone distance (e.g.,one extending from the target vehicle toward the front or rear of thehost vehicle—such as in the case that the host vehicle is driving towardthe target vehicle) may be at least one meter. A lateral buffer zonedistance (e.g., one extending from the target vehicle toward either sideof the host vehicle—such as when the host vehicle is traveling in a sameor opposite direction as the target vehicle such that a side of the hostvehicle will pass adjacent to a side of the target vehicle) may be atleast 0.5 meters.

As described above, other constraints may also be implicated bydetection of a target vehicle or a pedestrian in the environment of thehost vehicle. For example, the predicted trajectories of the hostvehicle and target vehicle 1217 may be considered and where the twotrajectories intersect (e.g., at intersection point 1230), a hardconstraint may require t₁ ^(l)>t₂ ^(a) or t₁ ^(l)>t₂ ^(a)+0.5 where thehost vehicle is vehicle 1, and target vehicle 1217 is vehicle 2.Similarly, the trajectory of pedestrian 1215 (based on a headingdirection and speed) may be monitored relative to the projectedtrajectory of the host vehicle. Given a particular pedestriantrajectory, with every point p on the trajectory, t(p) will representthe time required for the pedestrian to reach point p (i.e., point 1231in FIG. 12 ). To maintain the required buffer distance of at least 1meter from the pedestrian, either t(p) must be larger than the time thehost vehicle will reach point p (with sufficient difference in time suchthat the host vehicle passes in front of the pedestrian by a distance ofat least one meter) or that t(p) must be less than the time the hostvehicle will reach point p (e.g., if the host vehicle brakes to give wayto the pedestrian). Still, in the latter example, the hard constraintwill require that the host vehicle arrive at point p at a sufficienttime later than the pedestrian such that the host vehicle can passbehind the pedestrian and maintain the required buffer distance of atleast one meter.

Other hard constraints may also be employed. For example, a maximumdeceleration rate of the host vehicle may be employed in at least somecases. Such a maximum deceleration rate may be determined based on adetected distance to a target vehicle following the host vehicle (e.g.,using images collected from a rearward facing camera). The hardconstraints may include a mandatory stop at a sensed crosswalk or arailroad crossing or other applicable constraints.

Where analysis of a scene in an environment of the host vehicleindicates that one or more predefined navigational constraints may beimplicated, those constraints may be imposed relative to one or moreplanned navigational actions for the host vehicle. For example, whereanalysis of a scene results in driving policy module 803 returning adesired navigational action, that desired navigational action may betested against one or more implicated constraints. If the desirednavigational action is determined to violate any aspect of theimplicated constraints (e.g., if the desired navigational action wouldcarry the host vehicle within a distance of 0.7 meters of pedestrian1215 where a predefined hard constraint requires that the host vehicleremain at least 1.0 meters from pedestrian 1215), then at least onemodification to the desired navigational action may be made based on theone or more predefined navigational constraints. Adjusting the desirednavigational action in this way may provide an actual navigationalaction for the host vehicle in compliance with the constraintsimplicated by a particular scene detected in the environment of the hostvehicle.

After determination of the actual navigational action for the hostvehicle, that navigational action may be implemented by causing at leastone adjustment of a navigational actuator of the host vehicle inresponse to the determined actual navigational action for the hostvehicle. Such navigational actuator may include at least one of asteering mechanism, a brake, or an accelerator of the host vehicle.

Prioritized Constraints

As described above, various hard constraints may be employed with anavigational system to ensure safe operation of a host vehicle. Theconstraints may include a minimum safe driving distance with respect toa pedestrian, a target vehicle, a road barrier, or a detected object, amaximum speed of travel when passing within an influence zone of adetected pedestrian, or a maximum deceleration rate for the hostvehicle, among others. These constraints may be imposed with a trainedsystem trained based on machine learning (supervised, reinforcement, ora combination), but they also may be useful with non-trained systems(e.g., those employing algorithms to directly address anticipatedsituations arising in scenes from a host vehicle environment).

In either case, there may be a hierarchy of constraints. In other words,some navigational constraints may have priority over other constraints.Thus, if a situation arose in which a navigational action was notavailable that would result in all implicated constraints beingsatisfied, the navigation system may determine the availablenavigational action that achieves the highest priority constraintsfirst. For example, the system may cause the vehicle to avoid apedestrian first even if navigation to avoid the pedestrian would resultin a collision with another vehicle or an object detected in a road. Inanother example, the system may cause the vehicle to ride up on a curbto avoid a pedestrian.

FIG. 13 provides a flowchart illustrating an algorithm for implementinga hierarchy of implicated constraints determined based on analysis of ascene in an environment of a host vehicle. For example, at step 1301, atleast one processing device associated with the navigational system(e.g., an EyeQ processor, etc.) may receive, from a camera mounted onthe host vehicle, a plurality of images representative of an environmentof the host vehicle. Through analysis of an image or imagesrepresentative of the scene of the host vehicle environment at step1303, a navigational state associated with the host vehicle may beidentified. For example, a navigational state may indicate that the hostvehicle is traveling along a two-lane road 1210, as in FIG. 12 , that atarget vehicle 1217 is moving through an intersection ahead of the hostvehicle, that a pedestrian 1215 is waiting to cross the road on whichthe host vehicle travels, that an object 1219 is present ahead in thehost vehicle lane, among various other attributes of the scene.

At step 1305, one or more navigational constraints implicated by thenavigational state of the host vehicle may be determined. For example,the at least one processing device, after analyzing a scene in theenvironment of the host vehicle represented by one or more capturedimages may determine one or more navigational constraints implicated byobjects, vehicles, pedestrians, etc., recognized through image analysisof the captured images. In some embodiments, the at least one processingdevice may determine at least a first predefined navigational constraintand a second predefined navigational constraint implicated by thenavigational state, and the first predefined navigational constraint maydiffer from the second predefined navigational constraint. For example,the first navigational constraint may relate to one or more targetvehicles detected in the environment of the host vehicle, and the secondnavigational constraint may relate to a pedestrian detected in theenvironment of the host vehicle.

At step 1307, the at least one processing device may determine apriority associated with constraints identified in step 1305. In theexample described, the second predefined navigational constraint,relating to pedestrians, may have a priority higher than the firstpredefined navigational constraint, which relates to target vehicles.While priorities associated with navigational constraints may bedetermined or assigned based on various factors, in some embodiments,the priority of a navigational constraint may be related to its relativeimportance from a safety perspective. For example, while it may beimportant that all implemented navigational constraints be followed orsatisfied in as many situations as possible, some constraints may beassociated with greater safety risks than others and, therefore, may beassigned higher priorities. For example, a navigational constraintrequiring that the host vehicle maintain at least a 1 meter spacing froma pedestrian may have a higher priority than a constraint requiring thatthe host vehicle maintain at least a 1 meter spacing from a targetvehicle. This may be because a collision with a pedestrian may have moresevere consequences than a collision with another vehicle. Similarly,maintaining a space between the host vehicle and a target vehicle mayhave a higher priority than a constraint requiring the host vehicle toavoid a box in the road, to drive less than a certain speed over a speedbump, or to expose the host vehicle occupants to no more than a maximumacceleration level.

While driving policy module 803 is designed to maximize safety bysatisfying navigational constraints implicated by a particular scene ornavigational state, in some situations it may be physically impossibleto satisfy every implicated constraint. In such situations, the priorityof each implicated constraint may be used to determine which of theimplicated constraints should be satisfied first, as shown at step 1309.Continuing with the example above, in a situation where it is notpossible satisfy both the pedestrian gap constraint and the targetvehicle gap constraint, but rather only one of the constraints can besatisfied, then the higher priority of the pedestrian gap constraint mayresult in that constraint being satisfied before attempting to maintaina gap to the target vehicle. Thus, in normal situations, the at leastone processing device may determine, based on the identifiednavigational state of the host vehicle, a first navigational action forthe host vehicle satisfying both the first predefined navigationalconstraint and the second predefined navigational constraint where boththe first predefined navigational constraint and the second predefinednavigational constraint can be satisfied, as shown at step 1311. Inother situations, however, where not all the implicated constraints canbe satisfied, the at least one processing device may determine, based onthe identified navigational state, a second navigational action for thehost vehicle satisfying the second predefined navigational constraint(i.e., the higher priority constraint), but not satisfying the firstpredefined navigational constraint (having a priority lower than thesecond navigational constraint), where the first predefined navigationalconstraint and the second predefined navigational constraint cannot bothbe satisfied, as shown at step 1313.

Next, at step 1315, to implement the determined navigational actions forthe host vehicle the at least one processing device can cause at leastone adjustment of a navigational actuator of the host vehicle inresponse to the determined first navigational action or the determinedsecond navigational action for the host vehicle. As in previous example,the navigational actuator may include at least one of a steeringmechanism, a brake, or an accelerator.

Constraint Relaxation

As discussed above, navigational constraints may be imposed for safetypurposes. The constraints may include a minimum safe driving distancewith respect to a pedestrian, a target vehicle, a road barrier, or adetected object, a maximum speed of travel when passing within aninfluence zone of a detected pedestrian, or a maximum deceleration ratefor the host vehicle, among others. These constraints may be imposed ina learning or non-learning navigational system. In certain situations,these constraints may be relaxed. For example, where the host vehicleslows or stops near a pedestrian, then progresses slowly to convey anintention to pass by the pedestrian, a response of the pedestrian can bedetected from acquired images. If the response of the pedestrian is tostay still or to stop moving (and/or if eye contact with the pedestrianis sensed), it may be understood that the pedestrian recognizes anintent of the navigational system to pass by the pedestrian. In suchsituations, the system may relax one or more predefined constraints andimplement a less stringent constraint (e.g., allow the vehicle tonavigate within 0.5 meters of a pedestrian rather than within a morestringent 1 meter boundary).

FIG. 14 provides a flowchart for implementing control of the hostvehicle based on relaxation of one or more navigational constraints. Atstep 1401, the at least one processing device may receive, from a cameraassociated with the host vehicle, a plurality of images representativeof an environment of the host vehicle. Analysis of the images at step1403 may enable identification of a navigational state associated withthe host vehicle. At step 1405, the at least one processor may determinenavigational constraints associated with the navigational state of thehost vehicle. The navigational constraints may include a firstpredefined navigational constraint implicated by at least one aspect ofthe navigational state. At step 1407, analysis of the plurality ofimages may reveal the presence of at least one navigational constraintrelaxation factor.

A navigational constraint relaxation factor may include any suitableindicator that one or more navigational constraints may be suspended,altered, or otherwise relaxed in at least one aspect. In someembodiments, the at least one navigational constraint relaxation factormay include a determination (based on image analysis) that the eyes of apedestrian are looking in a direction of the host vehicle. In suchcases, it may more safely be assumed that the pedestrian is aware of thehost vehicle. As a result, a confidence level may be higher that thepedestrian will not engage in unexpected actions that cause thepedestrian to move into a path of the host vehicle. Other constraintrelaxation factors may also be used. For example, the at least onenavigational constraint relaxation factor may include: a pedestriandetermined to be not moving (e.g., one presumed to be less likely ofentering a path of the host vehicle); or a pedestrian whose motion isdetermined to be slowing. The navigational constraint relaxation factormay also include more complicated actions, such as a pedestriandetermined to be not moving after the host vehicle has come to a stopand then resumed movement. In such a situation, the pedestrian may beassumed to understand that the host vehicle has a right of way, and thepedestrian coming to a stop may suggest an intent of the pedestrian togive way to the host vehicle. Other situations that may cause one ormore constraints to be relaxed include the type of curb stone (e.g., alow curb stone or one with a gradual slope might allow a relaxeddistance constraint), lack of pedestrians or other objects on sidewalk,a vehicle with its engine not running may have a relaxed distance, or asituation in which a pedestrian is facing away and/or is moving awayfrom the area towards which the host vehicle is heading.

Where the presence of a navigational constraint relaxation factor isidentified (e.g., at step 1407), a second navigational constraint may bedetermined or developed in response to detection of the constraintrelaxation factor. This second navigational constraint may be differentfrom the first navigational constraint and may include at least onecharacteristic relaxed with respect to the first navigationalconstraint. The second navigational constraint may include a newlygenerated constraint based on the first constraint, where the newlygenerated constraint includes at least one modification that relaxes thefirst constraint in at least one respect. Alternatively, the secondconstraint may constitute a predetermined constraint that is lessstringent than the first navigational constraint in at least onerespect. In some embodiments, such second constraints may be reservedfor usage only for situations where a constraint relaxation factor isidentified in an environment of the host vehicle. Whether the secondconstraint is newly generated or selected from a set of fully orpartially available predetermined constraints, application of a secondnavigational constraint in place of a more stringent first navigationalconstraint (that may be applied in the absence of detection of relevantnavigational constraint relaxation factors) may be referred to asconstraint relaxation and may be accomplished in step 1409.

Where at least one constraint relaxation factor is detected at step1407, and at least one constraint has been relaxed in step 1409, anavigational action for the host vehicle may be determined at step 1411.The navigational action for the host vehicle may be based on theidentified navigational state and may satisfy the second navigationalconstraint. The navigational action may be implemented at step 1413 bycausing at least one adjustment of a navigational actuator of the hostvehicle in response to the determined navigational action.

As discussed above, the usage of navigational constraints and relaxednavigational constraints may be employed with navigational systems thatare trained (e.g., through machine learning) or untrained (e.g., systemsprogrammed to respond with predetermined actions in response to specificnavigational states). Where trained navigational systems are used, theavailability of relaxed navigational constraints for certainnavigational situations may represent a mode switching from a trainedsystem response to an untrained system response. For example, a trainednavigational network may determine an original navigational action forthe host vehicle, based on the first navigational constraint. The actiontaken by the vehicle, however, may be one that is different from thenavigational action satisfying the first navigational constraint.Rather, the action taken may satisfy the more relaxed secondnavigational constraint and may be an action developed by a non-trainedsystem (e.g., as a response to detection of a particular condition inthe environment of the host vehicle, such as the presence of anavigational constraint relaxation factor).

There are many examples of navigational constraints that may be relaxedin response to detection in the environment of the host vehicle of aconstraint relaxation factor. For example, where a predefinednavigational constraint includes a buffer zone associated with adetected pedestrian, and at least a portion of the buffer zone extends adistance from the detected pedestrian, a relaxed navigational constraint(either newly developed, called up from memory from a predetermined set,or generated as a relaxed version of a preexisting constraint) mayinclude a different or modified buffer zone. For example, the differentor modified buffer zone may have a distance relative to the pedestrianthat is less than the original or unmodified buffer zone relative to thedetected pedestrian. As a result, in view of the relaxed constraint, thehost vehicle may be permitted to navigate closer to a detectedpedestrian, where an appropriate constraint relaxation factor isdetected in the environment of the host vehicle.

A relaxed characteristic of a navigational constraint may include areduced width in a buffer zone associated with at least one pedestrian,as noted above. The relaxed characteristic, however, may also include areduced width in a buffer zone associated with a target vehicle, adetected object, a roadside barrier, or any other object detected in theenvironment of the host vehicle.

The at least one relaxed characteristic may also include other types ofmodifications in navigational constraint characteristics. For example,the relaxed characteristic may include an increase in speed associatedwith at least one predefined navigational constraint. The relaxedcharacteristic may also include an increase in a maximum allowabledeceleration/acceleration associated with at least one predefinednavigational constraint.

While constraints may be relaxed in certain situations, as describedabove, in other situations, navigational constraints may be augmented.For example, in some situations, a navigational system may determinethat conditions warrant augmentation of a normal set of navigationalconstraints. Such augmentation may include adding new constraints to apredefined set of constraints or adjusting one or more aspects of apredefined constraint. The addition or adjustment may result in moreconservative navigation relative the predefined set of constraintsapplicable under normal driving conditions. Conditions that may warrantconstraint augmentation may include sensor failure, adverseenvironmental conditions (rain, snow, fog, or other conditionsassociated with reduced visibility or reduced vehicle traction), etc.

FIG. 15 provides a flowchart for implementing control of the hostvehicle based on augmentation of one or more navigational constraints.At step 1501, the at least one processing device may receive, from acamera associated with the host vehicle, a plurality of imagesrepresentative of an environment of the host vehicle. Analysis of theimages at step 1503 may enable identification of a navigational stateassociated with the host vehicle. At step 1505, the at least oneprocessor may determine navigational constraints associated with thenavigational state of the host vehicle. The navigational constraints mayinclude a first predefined navigational constraint implicated by atleast one aspect of the navigational state. At step 1507, analysis ofthe plurality of images may reveal the presence of at least onenavigational constraint augmentation factor.

An implicated navigational constraint may include any of thenavigational constraints discussed above (e.g., with respect to FIG. 12) or any other suitable navigational constraints. A navigationalconstraint augmentation factor may include any indicator that one ormore navigational constraints may be supplemented/augmented in at leastone aspect. Supplementation or augmentation of navigational constraintsmay be performed on a per set basis (e.g., by adding new navigationalconstraints to a predetermined set of constraints) or may be performedon a per constraint basis (e.g., modifying a particular constraint suchthat the modified constraint is more restrictive than the original, oradding a new constraint that corresponds to a predetermined constraint,wherein the new constraint is more restrictive than the correspondingconstraint in at least one aspect). Additionally, or alternatively,supplementation or augmentation of navigational constraints may referselection from among a set of predetermined constraints based on ahierarchy. For example, a set of augmented constraints may be availablefor selection based on whether a navigational augmentation factor isdetected in the environment of or relative to the host vehicle. Undernormal conditions where no augmentation factor is detected, then theimplicated navigational constraints may be drawn from constraintsapplicable to normal conditions. On the other hand, where one or moreconstraint augmentation factors are detected, the implicated constraintsmay be drawn from augmented constraints either generated or predefinedrelative to the one or more augmentation factors. The augmentedconstraints may be more restrictive in at least one aspect thancorresponding constraints applicable under normal conditions.

In some embodiments, the at least one navigational constraintaugmentation factor may include a detection (e.g., based on imageanalysis) of the presence of ice, snow, or water on a surface of a roadin the environment of the host vehicle. Such a determination may bebased, for example, upon detection of: areas of reflectance higher thanexpected for dry roadways (e.g., indicative of ice or water on theroadway); white regions on the road indicating the presence of snow;shadows on the roadway consistent with the presence of longitudinaltrenches (e.g., tire tracks in snow) on the roadway; water droplets orice/snow particles on a windshield of the host vehicle; or any othersuitable indicator of the presence of water or ice/snow on a surface ofa road.

The at least one navigational constraint augmentation factor may alsoinclude detection of particulates on an outer surface of a windshield ofthe host vehicle. Such particulates may impair image quality of one ormore image capture devices associated with the host vehicle. Whiledescribed with respect to a windshield of the host vehicle, which isrelevant for cameras mounted behind the windshield of the host vehicle,detection of particulates on other surfaces (e.g., a lens or lens coverof a camera, headlight lens, rear windshield, a tail light lens, or anyother surface of the host vehicle visible to an image capture device (ordetected by a sensor) associated with the host vehicle may also indicatethe presence of a navigational constraint augmentation factor.

The navigational constraint augmentation factor may also be detected asan attribute of one or more image acquisition devices. For example, adetected decrease in image quality of one or more images captured by animage capture device (e.g., a camera) associated with the host vehiclemay also constitute a navigational constraint augmentation factor. Adecline in image quality may be associated with a hardware failure orpartial hardware failure associated with the image capture device or anassembly associated with the image capture device. Such a decline inimage quality may also be caused by environmental conditions. Forexample, the presence of smoke, fog, rain, snow, etc., in the airsurrounding the host vehicle may also contribute to reduced imagequality relative to the road, pedestrians, target vehicles, etc., thatmay be present in an environment of the host vehicle.

The navigational constraint augmentation factor may also relate to otheraspects of the host vehicle. For example, in some situations, thenavigational constraint augmentation factor may include a detectedfailure or partial failure of a system or sensor associate with the hostvehicle. Such an augmentation factor may include, for example, detectionof failure or partial failure of a speed sensor, GPS receiver,accelerometer, camera, radar, lidar, brakes, tires, or any other systemassociated with the host vehicle that may impact the ability of the hostvehicle to navigate relative to navigational constraints associated witha navigational state of the host vehicle.

Where the presence of a navigational constraint augmentation factor isidentified (e.g., at step 1507), a second navigational constraint may bedetermined or developed in response to detection of the constraintaugmentation factor. This second navigational constraint may bedifferent from the first navigational constraint and may include atleast one characteristic augmented with respect to the firstnavigational constraint. The second navigational constraint may be morerestrictive than the first navigational constraint, because detection ofa constraint augmentation factor in the environment of the host vehicleor associated with the host vehicle may suggest that the host vehiclemay have at least one navigational capability reduced with respect tonormal operating conditions. Such reduced capabilities may includelowered road traction (e.g., ice, snow, or water on a roadway; reducedtire pressure; etc.); impaired vision (e.g., rain, snow, dust, smoke,fog etc. that reduces captured image quality); impaired detectioncapability (e.g., sensor failure or partial failure, reduced sensorperformance, etc.), or any other reduction in capability of the hostvehicle to navigate in response to a detected navigational state.

Where at least one constraint augmentation factor is detected at step1507, and at least one constraint has been augmented in step 1509, anavigational action for the host vehicle may be determined at step 1511.The navigational action for the host vehicle may be based on theidentified navigational state and may satisfy the second navigational(i.e., augmented) constraint. The navigational action may be implementedat step 1513 by causing at least one adjustment of a navigationalactuator of the host vehicle in response to the determined navigationalaction.

As discussed, the usage of navigational constraints and augmentednavigational constraints may be employed with navigational systems thatare trained (e.g., through machine learning) or untrained (e.g., systemsprogrammed to respond with predetermined actions in response to specificnavigational states). Where trained navigational systems are used, theavailability of augmented navigational constraints for certainnavigational situations may represent a mode switching from a trainedsystem response to an untrained system response. For example, a trainednavigational network may determine an original navigational action forthe host vehicle, based on the first navigational constraint. The actiontaken by the vehicle, however, may be one that is different from thenavigational action satisfying the first navigational constraint.Rather, the action taken may satisfy the augmented second navigationalconstraint and may be an action developed by a non-trained system (e.g.,as a response to detection of a particular condition in the environmentof the host vehicle, such as the presence of a navigational constraintaugmented factor).

There are many examples of navigational constraints that may begenerated, supplemented, or augmented in response to detection in theenvironment of the host vehicle of a constraint augmentation factor. Forexample, where a predefined navigational constraint includes a bufferzone associated with a detected pedestrian, object, vehicle, etc., andat least a portion of the buffer zone extends a distance from thedetected pedestrian/object/vehicle, an augmented navigational constraint(either newly developed, called up from memory from a predetermined set,or generated as an augmented version of a preexisting constraint) mayinclude a different or modified buffer zone. For example, the differentor modified buffer zone may have a distance relative to thepedestrian/object/vehicle that is greater than the original orunmodified buffer zone relative to the detectedpedestrian/object/vehicle. As a result, in view of the augmentedconstraint, the host vehicle may be forced to navigate further from thedetected pedestrian/object/vehicle, where an appropriate constraintaugmentation factor is detected in the environment of the host vehicleor relative to the host vehicle.

The at least one augmented characteristic may also include other typesof modifications in navigational constraint characteristics. Forexample, the augmented characteristic may include a decrease in speedassociated with at least one predefined navigational constraint. Theaugmented characteristic may also include a decrease in a maximumallowable deceleration/acceleration associated with at least onepredefined navigational constraint.

Navigation Based on Long Range Planning

In some embodiments, the disclosed navigational system can respond notonly to a detected navigational state in an environment of the hostvehicle, but may also determine one or more navigational actions basedon long range planning. For example, the system may consider thepotential impact on future navigational states of one or morenavigational actions available as options for navigating with respect toa detected navigational state. Considering the effects of availableactions on future states may enable the navigational system to determinenavigational actions based not just upon a currently detectednavigational state, but also based upon long range planning. Navigationusing long range planning techniques may be especially applicable whereone or more reward functions are employed by the navigation system as atechnique for selecting navigational actions from among availableoptions. Potential rewards may be analyzed with respect to the availablenavigational actions that may be taken in response to a detected,current navigational state of the host vehicle. Further, however, thepotential rewards may also be analyzed relative to actions that may betaken in response to future navigational states projected to result fromthe available actions to a current navigational state. As a result, thedisclosed navigational system may, in some cases, select a navigationalaction in response to a detected navigational state even where theselected navigational action may not yield the highest reward from amongthe available actions that may be taken in response to the currentnavigational state. This may be especially true where the systemdetermines that the selected action may result in a future navigationalstate giving rise to one or more potential navigational actions offeringhigher rewards than the selected action or, in some cases, any of theactions available relative to a current navigational state. Theprinciple may be expressed more simply as taking a less favorable actionnow in order to produce higher reward options in the future. Thus, thedisclosed navigational system capable of long range planning may choosea suboptimal short term action where long term prediction indicates thata short term loss in reward may result in long term reward gains.

In general, autonomous driving applications may involve a series ofplanning problems, where the navigational system may decide on immediateactions in order to optimize a longer term Objective. For example, whena vehicle is confronted with a merge situation at a roundabout, thenavigational system may decide on an immediate acceleration or brakingcommand in order to initiate navigation into the roundabout. While theimmediate action to the detected navigational state at the roundaboutmay involve an acceleration or braking command responsive to thedetected state, the long term objective is a successful merge, and thelong term effect of the selected command is the success/failure of themerge. The planning problem may be addressed by decomposing the probleminto two phases. First, supervised learning may be applied forpredicting the near future based on the present (assuming the predictorwill be differentiable with respect to the representation of thepresent). Second, a full trajectory of the agent may be modeled using arecurrent neural network, where unexplained factors are modeled as(additive) input nodes. This may allow solutions to the long-termplanning problem to be determined using supervised learning techniquesand direct optimization over the recurrent neural network. Such anapproach may also enable the learning of robust policies byincorporating adversarial elements to the environment.

Two of the most fundamental elements of autonomous driving systems aresensing and planning. Sensing deals with finding a compactrepresentation of the present state of the environment, while planningdeals with deciding on what actions to take so as to optimize futureobjectives. Supervised machine learning techniques are useful forsolving sensing problems. Machine learning algorithmic frameworks mayalso be used for the planning part, especially reinforcement learning(RL) frameworks, such as those described above.

RL may be performed in a sequence of consecutive rounds. At round t, theplanner (a.k.a. the agent or driving policy module 803) may observe astate, s_(t)∈S, which represents the agent as well as the environment.It then should decide on an action a_(t)∈A. After performing the action,the agent receives an immediate reward, r_(t)∈

, and is moved to a new state, s_(t+1). As an example, the host vehiclemay include an adaptive cruise control (ACC) system, in which thevehicle should autonomously implement acceleration/braking so as to keepan adequate distance to a preceding vehicle while maintaining smoothdriving. The state can be modeled as a pair, s_(t)=(x_(t), v_(t))∈

², where x_(t) is the distance to the preceding vehicle and v_(t) is thevelocity of the host vehicle relative to the velocity of the precedingvehicle. The action a_(t) ∈

will be the acceleration command (where the host vehicle slows down ifa_(t)<0). The reward can be a function that depends on |a_(t)|(reflecting the smoothness of driving) and on s_(t) (reflecting that thehost vehicle maintains a safe distance from the preceding vehicle). Thegoal of the planner is to maximize the cumulative reward (maybe up to atime horizon or a discounted sum of future rewards), To do so, theplanner may rely on a policy, π:S→A, which maps a state into an action.

Supervised Learning (SL) can be viewed as a special case of RL, in whichs_(t) is sampled from some distribution over S, and the reward functionmay have the form r_(t)=

(a_(t),y_(t)), where

is a loss function, and the learner observes the value of y_(t) which isthe (possibly noisy) value of the optimal action to take when viewingthe state s_(t), There may be several differences between a general RLmodel and a specific case of SL, and these differences can make thegeneral RL problem more challenging.

In some SL situations, the actions (or predictions) taken by the learnermay have no effect on the environment. In other words, s_(t+1) and a_(t)are independent. This can have two important implications. First, in SL,a sample (s₁, y₁), . . . , (s_(m), y_(m)) can be collected in advance,and only then can the search begin for a policy (or predictor) that willhave good accuracy relative to the sample. In contrast, in RL, the states_(t+1) usually depends on the action taken (and also on the previousstate), Which in turn depends on the policy used to generate the action.This ties the data generation process to the policy learning process.Second, because actions do not affect the environment in SL, thecontribution of the choice of a_(t) to the performance of π is local.Specifically, a_(t) only affects the value of the immediate reward. Incontrast, in RL, actions that are taken at round t might have along-term effect on the reward values in future rounds.

In SL, the knowledge of the “correct” answer, y_(t), together with theshape of the reward, r_(t)=−

(a_(t), y_(t)) may provide full knowledge of the reward for all possiblechoices of a_(t), which may enable calculation of the derivative of thereward with respect to a_(t). In contrast, in RL, “one-shot” value ofthe reward may be all that can be observed for a specific choice ofaction taken. This may be referred to as a “bandit” feedback. This isone of the most significant reasons for the need of “exploration” as apart of long term navigational planning, because in RL-based systems, ifonly “bandit” feedback is available, the system may not always know ifthe action taken was the best action to take.

Many RL algorithms rely, at least in part, on the mathematically elegantmodel of a Markov Decision Process (MDP). The Markovian assumption isthat the distribution of s_(t+1) is fully determined given s_(t) anda_(t). This yields a closed form expression for the cumulative reward ofa given policy in terms of the stationary distribution over states ofthe MDP. The stationary distribution of a policy can be expressed as asolution to a linear programming problem. This yields two families ofalgorithms: 1) optimization with respect to the primal problem, whichmay be referred to as policy search, and 2) optimization with respect toa dual problem, whose variables are called the value function, V^(π).The value function determines the expected cumulative reward if the MDPbegins from the initial state, s, and from there actions are chosenaccording to π. A related quantity is the state-action value function,Q^(π)(s, a), which determines the cumulative reward assuming a startfrom state, s, an immediately chosen action a, and from there on actionschosen according to π. The Q function may give rise to acharacterization of the optimal policy (using the Bellman's equation).In particular, the Q function may show that the optimal policy is adeterministic function from S to A (in fact, it may be characterized asa “greedy” policy with respect to the optimal Q function).

One potential advantage of the MDP model is that it allows coupling ofthe future into the present using the Q function. For example, giventhat a host vehicle is now in state, s, the value of Q^(π)(s, a) mayindicate the effect of performing action a on the future. Therefore, theQ function may provide a local measure of the quality of an action a,thus making the RI, problem more similar to a SL scenario.

Many RL algorithms approximate the V function or the Q function in oneway or another. Value iteration algorithms, e.g., the Q learningalgorithm, may rely on the fact that the V and Q functions of theoptimal policy may be fixed points of some operators derived fromBellman's equation. Actor-critic policy iteration algorithms aim tolearn a policy in an iterative way, where at iteration t, the “critic”estimates Q^(π) ^(t) and based on this estimate, the “actor” improvesthe policy.

Despite the mathematical elegancy of MDPs and the convenience ofswitching to the Q function representation, this approach may haveseveral limitations. For example, an approximate notion of a Markovianbehaving state may be all that can be found in some cases. Furthermore,the transition of states may depend not only on the agent's action, butalso on actions of other players in the environment. For example, in theACC example mentioned above, while the dynamic of the autonomous vehiclemay be Markovian, the next state may depend on the behavior of thedriver of the other car, which is not necessarily Markovian. Onepossible solution to this problem is to use partially observed MDPs, inwhich it is assumed that there is a Markovian state, but an Observationthat is distributed according to the hidden state is what can be seen.

A more direct approach may consider game theoretical generalizations ofMDPs (e.g., the Stochastic Games framework). Indeed, algorithms for MDPsmay be generalized to multi-agents games (e.g., minimax-Q learning orNash-Q learning). Other approaches may include explicit modeling of theother players and vanishing regret learning algorithms. Learning in amulti-agent setting may be more complex than in a single agent setting.

A second limitation of the Q function representation may arise bydeparting from a tabular setting. The tabular setting is when the numberof states and actions is small, and therefore, Q can be expressed as atable with |S| rows and |A| columns. However, if the naturalrepresentation of S and A includes Euclidean spaces, and the state andaction spaces are discretized, the number of states/actions may beexponential in the dimension. In such cases, it may not be practical toemploy a tabular setting. Instead, the Q function may be approximated bysome function from a parametric hypothesis class (e.g., neural networksof a certain architecture). For example, a deep-Q-network (DQN) learningalgorithm may be used. In DQN, the state space can be continuous, butthe action space may remain a small discrete set. There may beapproaches for dealing with continuous action spaces, but they may relyon approximating the Q function. In any case, the Q function may becomplicated and sensitive to noise, and, therefore, may be challengingto learn.

A different approach may be to address the RL problem using a recurrentneural network (RNN). In some cases, RNN may be combined with thenotions of multi-agents games and robustness to adversarial environmentsfrom game theory. Further, this approach may be one that does notexplicitly rely on any Markovian assumption.

The following describes in more detail an approach for navigation byplanning based on prediction. In this approach, it may be assumed thatthe state space, S, is a subset of

^(d), and the action space, A, is a subset of

^(k). This may be a natural representation in many applications. Asnoted above, there may be two key differences between RL and SL: (1)because past actions affect future rewards, information from the futuremay need to be propagated back to the past; and (2) the “bandit” natureof rewards can blur the dependence between (state, action) and reward,which can complicate the learning process.

As a first step in the approach, an observation may be made that thereare interesting problems in Which the bandit nature of rewards is not anissue. For example, reward value (as will be discussed in more detailbelow) for the ACC application may be differentiable with respect to thecurrent state and action. In fact, even if the reward is given in a“bandit” manner, the problem of learning a differentiable function,{circumflex over (r)}(s, a), such that {circumflex over (r)}(s_(t),a_(t))≈r_(t), may be a relatively straightforward SL problem (e.g., aone dimensional regression problem). Therefore, the first step of theapproach may be to either define the reward as a function, {circumflexover (r)}(s, a), which is differentiable with respect to s and a, or touse a regression learning algorithm in order to learn a differentiablefunction, {circumflex over (r)}, that minimizes at least some regressionloss over a sample with instance vector being (s_(t), a_(t))∈

^(d)×

^(k) and target scalar being r_(t). In some situations, in order tocreate a training set, elements of exploration may be used.

To address the connection between past and future, a similar idea may beused. For example, suppose a differentiable function {circumflex over(N)}(s, a) can be learned such that {circumflex over (N)}(s_(t),a_(t))≈s_(t+1). Learning such a function may be characterized as an SLproblem. {circumflex over (N)} may be viewed as a predictor for the nearfuture. Next, a policy that maps from S to A may be described using aparametric function π_(θ):S→S Expressing π_(θ) as a neural network, mayenable expression of an episode of running the agent for T rounds usinga recurrent neural network (RNN), where the next state is defined ass_(t+1)={circumflex over (N)}(s_(t), a_(t))+v_(t). Here, v_(t)∈

^(d) may be defined by the environment and may express unpredictableaspects of the near future. The fact that s_(t+1) depends on s_(t) anda_(t) in a differentiable manner may enable a connection between futurereward values and past actions. A parameter vector of the policyfunction, π_(θ), may be learned by back-propagation over the resultingRNN. Note that explicit probabilistic assumptions need not be imposed onν_(t). In particular, there need not be a requirement for a Markovianrelation. Instead, the recurrent network may be relied upon to propagate“enough” information between past and future. Intuitively, {circumflexover (N)}(s_(t), a_(t)) may describe the predictable part of the nearfuture, while ν_(t) may express the unpredictable aspects, which mayarise due to the behavior of other players in the environment. Thelearning system should learn a policy that will be robust to thebehavior of other players. If ∥ν₁∥ is large, the connection between pastactions and future reward values may be too noisy for learning ameaningful policy. Explicitly expressing the dynamic of the system in atransparent way may enable incorporation of prior knowledge more easily.For example, prior knowledge may simplify the problem of defining{circumflex over (N)}.

As discussed above, the learning system may benefit from robustnessrelative to an adversarial environment, such as the environment of ahost vehicle, which may include multiple other drivers that may act inunexpected way. In a model that does not impose probabilisticassumptions on ν_(t), environments may be considered in which ν_(t) ischosen in an adversarial manner. In some cases, restrictions may beplaced on μ_(t), otherwise the adversary can make the planning problemdifficult or even impossible. One natural restriction may be to requirethat ∥μ_(t)∥ is bounded by a constant.

Robustness against adversarial environments may be useful in autonomousdriving applications. Choosing μ t in an adversarial way may even speedup the learning process, as it can focus the learning system toward arobust optimal policy. A simple game may be used to illustrate thisconcept. The state is s_(t)∈

, the action is a_(t)∈

, and the immediate loss function is 0.1|a_(t)|+[|s_(t)|−2]₊, where[x]₊=max{x, 0} is the ReLU (rectified linear unit) function. The nextstate is s_(t+1)=s_(t)+a_(t)+ν_(t), where ν_(t)∈[−0.5, 0.5] is chosenfor the environment in an adversarial manner. Here, the optimal policymay be written as a two layer network with ReLU:a_(t)=−[s_(t)−1.5]₊+[−s_(t)−1.5]₊. Observe that when |s_(t)|∈(1.5, 2],the optimal action may have a larger immediate loss than the action a=0.Therefore, the system may plan for the future and may not rely solely onthe immediate loss. Observe that the derivative of the loss with respectto a_(t) is 0.1 sign (a_(t)), and the derivative with respect to s_(t)is 1[|s_(t)|>2]sign(s_(t)). In a situation in which s_(t)∈(1.5.2], theadversarial choice of ν_(t) would be to set ν_(t)=0.5 and, therefore,there may be a non-zero loss on round t+1, whenever a_(t)>1.5−s_(t). Insuch cases, the derivative of the loss may back-propagate directly toa_(t). Thus, the adversarial choice of ν_(t) may help the navigationalsystem obtain a non-zero back-propagation message in cases for which thechoice of a_(t) is sub optimal. Such a relationship may aid thenavigational system in selecting present actions based on an expectationthat such a present action (even if that action would result in asuboptimal reward or even a loss) will provide opportunities in thefuture for more optimal actions that result in higher rewards.

Such an approach may be applied to virtually any navigational situationthat may arise. The following describes the approach applied to oneexample: adaptive cruise control (ACC). In the ACC problem, the hostvehicle may attempt to maintain an adequate distance to a target vehicleahead (e.g., 1.5 seconds to the target car). Another goal may be todrive as smooth as possible while maintaining the desired gap. A modelrepresenting this situation may be defined as follows. The state spaceis

R³, and the action space is

. The first coordinate of the state is the speed of the target car, thesecond coordinate is the speed of the host vehicle, and the lastcoordinate is the distance between the host vehicle and target vehicle(e.g., location of the host vehicle minus the location of the targetalong the road curve). The action to be taken by the host vehicle is theacceleration, and may be denoted by a_(t). The quantity τ may denote thedifference in time between consecutive rounds. While T may be set to anysuitable quantity, in one example, T may be 0.1 seconds. Position,s_(t), may be denoted as s_(t)=(v_(t) ^(target), v_(t) ^(host), x_(t))and the (unknown) acceleration of the target vehicle may be denoted asa_(t) ^(target).

The full dynamics of the system can be described by:v _(t) ^(target) =[v _(t−1) ^(target) +τa _(t−1) ^(target)]+v _(t) ^(host) =[v _(t−1) ^(host) +τa _(t−1) ^(host)]+x _(t) =[x _(t−1)+τ(v _(t−1) ^(target) −v _(i−1) ^(host))]+

This can be described as a sum of two vectors:

$s_{t} = {( {\lbrack {{s_{t - 1}\lbrack 0\rbrack} + {\tau\; a_{t - 1}^{target}}} \rbrack_{+}.\lbrack {{s_{t - 1}\lbrack 1\rbrack} + {\tau\; a_{t - 1}}} \rbrack_{+}.\lbrack {{s_{t - 1}\lbrack 0\rbrack} + {\tau\;( {{s_{t - 1}\lbrack 0\rbrack} - {s_{t - 1}\lbrack 1\rbrack}} )}} \rbrack_{+}} ) = {\underset{\underset{N{({s_{t - 1},a_{t}})}}{︸}}{( {{s_{t - 1}\lbrack 0\rbrack},\lbrack {{s_{t - 1}\lbrack 1\rbrack} + {\tau\; a_{t - 1}}} \rbrack_{+},\lbrack {{s_{t - 1}\lbrack 2\rbrack} + {\tau( {{s_{t - 1}\lbrack 0\rbrack} - {s_{t - 1}\lbrack 1\rbrack}} )}} \rbrack_{+}} )} + \underset{\underset{v_{t}}{︸}}{( {{\lbrack {{s_{t - 1}\lbrack 0\rbrack} + {\tau\; a_{t - 1}^{target}}} \rbrack_{+} - {s_{t - 1}\lbrack 0\rbrack}},0,0} )}}}$

The first vector is the predictable part, and the second vector is theunpredictable part. The reward on round t is defined as follows:−r _(t)=0.1|a _(t) |+[∥x _(t) /x _(t)*−1|−0.3]₊ where x _(t)*=max{1,1.5v_(t) ^(host)}

The first term may result in a penalty for non-zero accelerations, thusencouraging smooth driving. The second term depends on the ratio betweenthe distance to the target car, x_(t), and the desired distance, x_(t)*,which is defined as the maximum between a distance of 1 meter and breakdistance of 1.5 seconds. In some cases, this ratio may be exactly 1, butas long as this ratio is within [0.7, 1.3], the policy may forego anypenalties, which may allow the host vehicle some slack in navigation—acharacteristic that may be important in achieving a smooth drive.

Implementing the approach outlined above, the navigation system of thehost vehicle (e.g., through operation of driving policy module 803within processing unit 110 of the navigation system) may select anaction in response to an Observed state. The selected action may bebased on analysis not only of rewards associated with the responsiveactions available relative to a sensed navigational state, but may alsobe based on consideration and analysis of future states, potentialactions in response to the futures states, and rewards associated withthe potential actions.

FIG. 16 illustrates an algorithmic approach to navigation based ondetection and long range planning. For example, at step 1601, the atleast one processing device 110 of the navigation system for the hostvehicle may receive a plurality of images. These images may capturescenes representative of an environment of the host vehicle and may besupplied by any of the image capture devices (e.g., cameras, sensors,etc.) described above. Analysis of one or more of these images at step1603 may enable the at least one processing device 110 to identify apresent navigational state associated with the host vehicle (asdescribed above).

At steps 1605, 1607, and 1609, various potential navigational actionsresponsive to the sensed navigational state may be determined. Thesepotential navigational actions (e.g., a first navigational actionthrough an N^(th) available navigational action) may be determined basedon the sensed state and the long range goals of the navigational system(e.g., to complete a merge, follow a lead vehicle smoothly, pass atarget vehicle, avoid an object in the roadway, slow for a detected stopsign, avoid a target vehicle cutting in, or any other navigationalaction that may advance the navigational goals of the system).

For each of the determined potential navigational actions, the systemmay determine an expected reward. The expected reward may be determinedaccording to any of the techniques described above and may includeanalysis of a particular potential action relative to one or more rewardfunctions. Expected rewards 1606, 1608, and 1610 may be determined foreach of the potential navigational actions (e.g., the first, second, andN^(th)) determined in steps 1605, 1607, and 1609, respectively.

In some cases, the navigational system of the host vehicle may selectfrom among the available potential actions based on values associatedwith expected rewards 1606, 1608, and 1610 (or any other type ofindicator of an expected reward). For example, in some situations, theaction that yields the highest expected reward may be selected.

In other cases, especially where the navigation system engages in longrange planning to determine navigational actions for the host vehicle,the system may not choose the potential action that yields the highestexpected reward. Rather, the system may look to the future to analyzewhether there may be opportunities for realizing higher rewards later iflower reward actions are selected in response to a current navigationalstate. For example, for any or all of the potential actions determinedat steps 1605, 1607, and 1609, a future state may be determined. Eachfuture state, determined at steps 1613, 1615, and 1617, may represent afuture navigational state expected to result based on the currentnavigational state as modified by a respective potential action (e.g.,the potential actions determined at steps 1605, 1607, and 1609).

For each of the future states predicted at steps 1613, 1615, and 1617,one or more future actions (as navigational options available inresponse to determined future state) may be determined and evaluated. Atsteps 1619, 1621, and 1623, for example, values or any other type ofindicator of expected rewards associated with one or more of the futureactions may be developed (e.g., based on one or more reward functions).The expected rewards associated with the one or more future actions maybe evaluated by comparing values of reward functions associated witheach future action or by comparing any other indicators associated withthe expected rewards.

At step 1625, the navigational system for the host vehicle may select anavigational action for the host vehicle based on a comparison ofexpected rewards, not just based on the potential actions identifiedrelative to a current navigational state (e.g., at steps 1605, 1607, and1609), but also based on expected rewards determined as a result ofpotential future actions available in response to predicted futurestates (e.g., determined at steps 1613, 1615, and 1617). The selectionat step 1625 may be based on the options and rewards analysis performedat steps 1619, 1621, and 1623.

The selection of a navigational action at step 1625 may be based on acomparison of expected rewards associated with future action optionsonly. In such a case, the navigational system may select an action tothe current state based solely on a comparison of expected rewardsresulting from actions to potential future navigational states. Forexample, the system may select the potential action identified at step1605, 1607, or 1609 that is associated with a highest future rewardvalue as determined through analysis at steps 1619, 1621, and 1623.

The selection of a navigational action at step 1625 may also be based oncomparison of current action options only (as noted above). In thissituation, the navigational system may select the potential actionidentified at step 1605, 1607, or 1609 that is associated with a highestexpected reward, 1606, 1608, or 1610. Such a selection may be performedwith little or no consideration of future navigational states or futureexpected rewards to navigational actions available in response toexpected future navigational states.

On the other hand, in some cases, the selection of a navigational actionat step 1625 may be based on a comparison of expected rewards associatedwith both future action options and with current action options. This,in fact, may be one of the principles of navigation based on long rangeplanning. For example, expected rewards to future actions may beanalyzed to determine if any may warrant a selection of a lower rewardaction in response to the current navigational state in order to achievea potential higher reward in response to a subsequent navigationalaction expected to be available in response to future navigationalstates. As an example, a value or other indicator of an expected reward1606 may indicate a highest expected reward from among rewards 1606,1608, and 1610. On the other hand, expected reward 1608 may indicate alowest expected reward from among rewards 1606, 1608, and 1610. Ratherthan simply selecting the potential action determined at step 1605(i.e., the action giving rise to the highest expected reward 1606),analysis of future states, potential future actions, and future rewardsmay be used in making a navigational action selection at step 1625. Inone example, it may be determined that a reward identified at step 1621(in response to at least one future action to a future state determinedat step 1615 based on the second potential action determined at step1607) may be higher than expected reward 1606. Based on this comparison,the second potential action determined at step 1607 may be selectedrather than the first potential action determined at step 1605 despiteexpected reward 1606 being higher than expected reward 1608. In oneexample, the potential navigational action determined at step 1605 mayinclude a merge in front of a detected target vehicle, while thepotential navigational action determined at step 1607 may include amerge behind the target vehicle. While the expected reward 1606 ofmerging in front of the target vehicle may be higher than the expectedreward 1608 associated with merging behind the target vehicle, it may bedetermined that merging behind the target vehicle may result in a futurestate for which there may be action options yielding even higherpotential rewards than expected reward 1606, 1608, or other rewardsbased on available actions in response to a current, sensed navigationalstate.

Selection from among potential actions at step 1625 may be based on anysuitable comparison of expected rewards (or any other metric orindicator of benefits associated with one potential action overanother). In some cases, as described above, a second potential actionmay be selected over a first potential action if the second potentialaction is projected to provide at least one future action associatedwith an expected reward higher than a reward associated with the firstpotential action. In other cases, more complex comparisons may beemployed. For example, rewards associated with action options inresponse to projected future states may be compared to more than oneexpected reward associated with a determined potential action.

In some scenarios, actions and expected rewards based on projectedfuture states may affect selection of a potential action to a currentstate if at least one of the future actions is expected to yield areward higher than any of the rewards expected as a result of thepotential actions to a current state (e.g., expected rewards 1606, 1608,1610, etc.). In some cases, the future action option that yields thehighest expected reward (e.g., from among the expected rewardsassociated with potential actions to a sensed current state as well asfrom among expected rewards associated with potential future actionoptions relative to potential future navigational states) may be used asa guide for selection of a potential action to a current navigationalstate. That is, after identifying a future action option yielding thehighest expected reward (or a reward above a predetermined threshold,etc.), the potential action that would lead to the future stateassociated with the identified future action yielding the highestexpected reward may be selected at step 1625.

In other cases, selection of available actions may be made based ondetermined differences between expected rewards. For example, a secondpotential action determined at step 1607 may be selected if a differencebetween an expected reward associated with a future action determined atstep 1621 and expected reward 1606 is greater than a difference betweenexpected reward 1608 and expected reward 1606 (assuming+signdifferences). In another example, a second potential action determinedat step 1607 may be selected if a difference between an expected rewardassociated with a future action determined at step 1621 and an expectedreward associated with a future action determined at step 1619 isgreater than a difference between expected reward 1608 and expectedreward 1606.

Several examples have been described for selecting from among potentialactions to a current navigational state. Any other suitable comparisontechnique or criteria, however, may be used for selecting an availableaction through long range planning based on action and reward analysisextending to projected future states. Additionally, while FIG. 16represents two layers in the long range planning analysis (e.g., a firstlayer considering the rewards resulting from potential actions to acurrent state, and a second layer considering the rewards resulting fromfuture action options in response to projected future states), analysisbased on more layers may be possible. For example, rather than basingthe long range planning analysis upon one or two layers, three, four ormore layers of analysis could be used in selecting from among availablepotential actions in response to a current navigational state.

After a selection is made from among potential actions in response to asensed navigational state, at step 1627, the at least one processor maycause at least one adjustment of a navigational actuator of the hostvehicle in response to the selected potential navigational action. Thenavigational actuator may include any suitable device for controlling atleast one aspect of the host vehicle. For example, the navigationalactuator may include at least one of a steering mechanism, a brake, oran accelerator.

Navigation Based on Inferred Aggression of Others

Target vehicles may be monitored through analysis of an acquired imagestream to determine indicators of driving aggression. Aggression isdescribed herein as a qualitative or quantitative parameter, but othercharacteristics may be used: perceived level of attention (potentialimpairment of driver, distracted-cell phone, asleep, etc.). In somecases, a target vehicle may be deemed to have a defensive posture, andin some cases, the target vehicle may be determined to have a moreaggressive posture. Navigational actions may be selected or developedbased on indicators of aggression. For example, in some cases, therelative velocity, relative acceleration, increases in relativeacceleration, following distance, etc., relative to a host vehicle maybe tracked to determine if the target vehicle is aggressive ordefensive. If the target vehicle is determined to have a level ofaggression exceeding a threshold, for example, the host vehicle may beinclined to give way to the target vehicle. A level of aggression of thetarget vehicle may also be discerned based on a determined behavior ofthe target vehicle relative to one or more obstacles in a path of or ina vicinity of the target vehicle (e.g., a leading vehicle, obstacle inthe road, traffic light, etc.).

As an introduction to this concept, an example experiment will bedescribed with respect to a merger of the host vehicle into aroundabout, in which a navigational goal is to pass through and out ofthe roundabout. The situation may begin with the host vehicle approachesan entrance of the roundabout and may end with the host vehicle reachesan exit of the roundabout (e.g., the second exit). Success may bemeasured based on whether the host vehicle maintains a safe distancefrom all other vehicles at all times, whether the host vehicle finishesthe route as quickly as possible, and whether the host vehicle adheresto a smooth acceleration policy. In this illustration, N_(T) targetvehicles may be placed at random on the roundabout. To model a blend ofadversarial and typical behavior, with probability p, a target vehiclemay be modeled by an “aggressive” driving policy, such that theaggressive target vehicle accelerates when the host vehicle attempts tomerge in front of the target vehicle. With probability 1-p, the targetvehicle may be modeled by a “defensive” driving policy, such that thetarget vehicle decelerates and lets the host vehicle merge in. In thisexperiment, p=0.5, and the navigation system of the host vehicle may beprovided with no information about the type of the other drivers. Thetypes of other drivers may be chosen at random at the beginning of theepisode.

The navigational state may be represented as the velocity and locationof the host vehicle (the agent), and the locations, velocities, andaccelerations of the target vehicles. Maintaining target accelerationobservations may be important in order to differentiate betweenaggressive and defensive drivers based on the current state. All targetvehicles may move on a one-dimensional curve that outlines theroundabout path. The host vehicle may move on its own one-dimensionalcurve, which intersects the target vehicles' curve at the merging point,and this point is the origin of both curves. To model reasonabledriving, the absolute value of all vehicles' accelerations may be upperbounded by a constant. Velocities may also be passed through a ReLUbecause driving backward is not allowed. Note that by not allowingdriving backwards, long-term planning may become a necessity, as theagent cannot regret on its past actions.

As described above, the next state, s_(t+1), may be decomposed into asum of a predictable part, {circumflex over (N)}(s_(t), a_(t)), and anon-predictable part, ν_(t). The expression, {circumflex over(N)}(s_(t), a_(t)), may represent the dynamics of vehicle locations andvelocities (which may be well-defined in a differentiable manner), whileν_(t) may represent the target vehicles' acceleration. It may beverified that {circumflex over (N)}(s_(t), a_(t)) can be expressed as acombination of ReLU functions over an affine transformation, hence it isdifferentiable with respect to s_(t) and a_(t). The vector ν_(t) may bedefined by a simulator in a non-differentiable manner, and may implementaggressive behavior for some targets and defensive behavior for othertargets. Two frames from such a simulator are shown in FIGS. 17A and17B. In this example experiment, a host vehicle 1701 learned to slowdownas it approached the entrance of the roundabout. It also learned to giveway to aggressive vehicles (e.g., vehicles 1703 and 1705), and to safelycontinue when merging in front of defensive vehicles (e.g., vehicles1706, 1708, and 1710). In the example represented by FIGS. 17A and 17B,the navigation system of host vehicle 1701 is not provided with the typeof target vehicles. Rather, whether a particular vehicle is determinedto be aggressive or defensive is determined through inference based onobserved position and acceleration, for example, of the target vehicles.In FIG. 17A, based on position, velocity, and/or relative acceleration,host vehicle 1701 may determine that vehicle 1703 has an aggressivetendency and, therefore, host vehicle 1701 may stop and wait for targetvehicle 1703 to pass rather than attempting to merge in front of targetvehicle 1703. In FIG. 17B, however, target vehicle 1701 recognized thatthe target vehicle 1710 traveling behind vehicle 1703 exhibiteddefensive tendencies (again, based on observed position, velocity,and/or relative acceleration of vehicle 1710) and, therefore, completeda successful merge in front of target vehicle 1710 and behind targetvehicle 1703.

FIG. 18 provides a flowchart representing an example algorithm fornavigating a host vehicle based on predicted aggression of othervehicles. In the example of FIG. 18 , a level of aggression associatedwith at least one target vehicle may be inferred based on observedbehavior of the target vehicle relative to an object in the environmentof the target vehicle. For example, at step 1801, at least oneprocessing device (e.g., processing device 110) of the host vehiclenavigation system may receive, from a camera associated with the hostvehicle, a plurality of images representative of an environment of thehost vehicle. At step 1803, analysis of one or more of the receivedimages may enable the at least one processor to identify a targetvehicle (e.g., vehicle 1703) in the environment of the host vehicle1701. At step 1805, analysis of one or more of the received images mayenable the at least one processing device to identify in the environmentof the host vehicle at least one obstacle to the target vehicle. Theobject may include debris in a roadway, a stoplight/traffic light, apedestrian, another vehicle (e.g., a vehicle traveling ahead of thetarget vehicle, a parked vehicle, etc.), a box in the roadway, a roadbarrier, a curb, or any other type of object that may be encountered inan environment of the host vehicle. At step 1807, analysis of one ormore of the received images may enable the at least one processingdevice to determine at least one navigational characteristic of thetarget vehicle relative to the at least one identified obstacle to thetarget vehicle.

Various navigational characteristics may be used to infer a level ofaggression of a detected target vehicle in order to develop anappropriate navigational response to the target vehicle. For example,such navigational characteristics may include a relative accelerationbetween the target vehicle and the at least one identified obstacle, adistance of the target vehicle from the obstacle (e.g., a followingdistance of the target vehicle behind another vehicle), and/or arelative velocity between the target vehicle and the obstacle, etc.

In some embodiments, the navigational characteristics of the targetvehicles may be determined based on outputs from sensors associated withthe host vehicle (e.g., radar, speed sensors, GPS, etc.). In some cases,however, the navigational characteristics of the target vehicles may bedetermined partially or fully based on analysis of images of anenvironment of the host vehicle. For example, image analysis techniquesdescribed above and in, for example, U.S. Pat. No. 9,168,868, which isincorporated herein by reference, may be used to recognize targetvehicles within an environment of the host vehicle. And, monitoring alocation of a target vehicle in the captured images over time and/ormonitoring locations in the captured images of one or more featuresassociated with the target vehicle (e.g., tail lights, head lights,bumper, wheels, etc.) may enable a determination of relative distances,velocities, and/or accelerations between the target vehicles and thehost vehicle or between the target vehicles and one or more otherobjects in an environment of the host vehicle.

An aggression level of an identified target vehicle may be inferred fromany suitable observed navigational characteristic of the target vehicleor any combination of observed navigational characteristics. Forexample, a determination of aggressiveness may be made based on anyobserved characteristic and one or more predetermined threshold levelsor any other suitable qualitative or quantitative analysis. In someembodiments, a target vehicle may be deemed as aggressive if the targetvehicle is observed to be following the host vehicle or another vehicleat a distance less than a predetermined aggressive distance threshold.On the other hand, a target vehicle observed to be following the hostvehicle or another vehicle at a distance greater than a predetermineddefensive distance threshold may be deemed defensive. The predeterminedaggressive distance threshold need not be the same as the predetermineddefensive distance threshold. Additionally, either or both of thepredetermined aggressive distance threshold and the predetermineddefensive distance threshold may include a range of values, rather thana bright line value. Further, neither of the predetermined aggressivedistance threshold nor the predetermined defensive distance thresholdmust be fixed. Rather these values, or ranges of values, may shift overtime, and different thresholds/ranges of threshold values may be appliedbased on observed characteristics of a target vehicle. For example, thethresholds applied may depend on one or more other characteristics ofthe target vehicle. Higher observed relative velocities and/oraccelerations may warrant application of larger threshold values/ranges.Conversely, lower relative velocities and/or accelerations, includingzero relative velocities and/or accelerations, may warrant applicationof smaller distance threshold values/ranges in making theaggressive/defensive inference.

The aggressive/defensive inference may also be based on relativevelocity and/or relative acceleration thresholds. A target vehicle maybe deemed aggressive if its observed relative velocity and/or itsrelative acceleration with respect to another vehicle exceeds apredetermined level or range. A target vehicle may be deemed defensiveif its observed relative velocity and/or its relative acceleration withrespect to another vehicle falls below a predetermined level or range.

While the aggressive/defensive determination may be made based on anyobserved navigational characteristic alone, the determination may alsodepend on any combination of observed characteristics. For example, asnoted above, in some cases, a target vehicle may be deemed aggressivebased solely on an observation that it is following another vehicle at adistance below a certain threshold or range. In other cases, however,the target vehicle may be deemed aggressive if it both follows anothervehicle at less than a predetermined amount (which may be the same as ordifferent than the threshold applied where the determination is based ondistance alone) and has a relative velocity and/or a relativeacceleration of greater than a predetermined amount or range. Similarly,a target vehicle may be deemed defensive based solely on an observationthat it is following another vehicle at a distance greater than acertain threshold or range. In other cases, however, the target vehiclemay be deemed defensive if it both follows another vehicle at greaterthan a predetermined amount (which may be the same as or different thanthe threshold applied where the determination is based on distancealone) and has a relative velocity and/or a relative acceleration ofless than a predetermined amount or range. System 100 may make anaggressive/defensive if, for example, a vehicle exceeds 0.5 Gacceleration or deceleration (e.g., jerk 5 m/s3), a vehicle has alateral acceleration of 0.5 G in a lane change or on a curve, a vehiclecauses another vehicle to do any of the above, a vehicle changes lanesand causes another vehicle to give way by more than 0.3 G decelerationor jerk of 3 m/s3, and/or a vehicle changes two lanes without stopping.

It should be understood that references to a quantity exceeding a rangemay indicate that the quantity either exceeds all values associated withthe range or falls within the range. Similarly, references to a quantityfalling below a range may indicate that the quantity either falls belowall values associated with the range or falls within the range.Additionally, while the examples described for making anaggressive/defensive inference are described with respect to distance,relative acceleration, and relative velocity, any other suitablequantities may be used. For example, a time to collision may calculationmay be used or any indirect indicator of distance, acceleration, and/orvelocity of the target vehicle. It should also be noted that while theexamples above focus on target vehicles relative to other vehicles, theaggressive/defensive inference may be made by observing the navigationalcharacteristics of a target vehicle relative to any other type ofobstacle (e.g., a pedestrian, road barrier, traffic light, debris,etc.).

Returning to the example shown in FIGS. 17A and 17B, as host vehicle1701 approaches the roundabout, the navigation system, including its atleast one processing device, may receive a stream of images from acamera associated with the host vehicle. Based on analysis of one ormore of the received images, any of target vehicles 1703, 1705, 1706,1708, and 1710 may be identified. Further, the navigation system mayanalyze the navigational characteristics of one or more of theidentified target vehicles. The navigation system may recognize that thegap between target vehicles 1703 and 1705 represents the firstopportunity for a potential merge into the roundabout. The navigationsystem may analyze target vehicle 1703 to determine indicators ofaggression associated with target vehicle 1703. If target vehicle 1703is deemed aggressive, then the host vehicle navigation system may chooseto give way to vehicle 1703 rather than merging in front of vehicle1703. On the other hand, if target vehicle 1703 is deemed defensive,then the host vehicle navigation system may attempt to complete a mergeaction ahead of vehicle 1703.

As host vehicle 1701 approaches the roundabout, the at least oneprocessing device of the navigation system may analyze the capturedimages to determine navigational characteristics associated with targetvehicle 1703. For example, based on the images, it may be determinedthat vehicle 1703 is following vehicle 1705 at a distance that providesa sufficient gap for the host vehicle 1701 to safely enter. Indeed, itmay be determined that vehicle 1703 is following vehicle 1705 by adistance that exceeds an aggressive distance threshold, and therefore,based on this information, the host vehicle navigation system may beinclined to identify target vehicle 1703 as defensive. In somesituations, however, more than one navigational characteristic of atarget vehicle may be analyzed in making the aggressive/defensivedetermination, as discussed above. Furthering the analysis, the hostvehicle navigation system may determine that, while target vehicle 1703is following at a non-aggressive distance behind target vehicle 1705,vehicle 1703 has a relative velocity and/or a relative acceleration withrespect to vehicle 1705 that exceeds one or more thresholds associatedwith aggressive behavior. Indeed, host vehicle 1701 may determine thattarget vehicle 1703 is accelerating relative to vehicle 1705 and closingthe gap that exists between vehicles 1703 and 1705. Based on furtheranalysis of the relative velocity, acceleration, and distance (and evena rate that the gap between vehicles 1703 and 1705 is closing), hostvehicle 1701 may determine that target vehicle 1703 is behavingaggressively. Thus, while there may be a sufficient gap into which hostvehicle may safely navigate, host vehicle 1701 may expect that a mergein front of target vehicle 1703 would result in an aggressivelynavigating vehicle directly behind the host vehicle. Further, targetvehicle 1703 may be expected, based on the observed behavior throughimage analysis or other sensor output, that target vehicle 1703 wouldcontinue accelerating toward host vehicle 1701 or continuing toward hostvehicle 1701 at a non-zero relative velocity if host vehicle 1701 was tomerge in front of vehicle 1703. Such a situation may be undesirable froma safety perspective and may also result in discomfort to passengers ofthe host vehicle. For such reasons, host vehicle 1701 may choose to giveway to vehicle 1703, as shown in FIG. 17B, and merge into the roundaboutbehind vehicle 1703 and in front of vehicle 1710, deemed defensive basedon analysis of one or more of its navigational characteristics.

Returning to FIG. 18 , at step 1809, the at least one processing deviceof the navigation system of the host vehicle may determine, based on theidentified at least one navigational characteristic of the targetvehicle relative to the identified obstacle, a navigational action forthe host vehicle (e.g., merge in front of vehicle 1710 and behindvehicle 1703). To implement the navigational action (at step 1811), theat least one processing device may cause at least one adjustment of anavigational actuator of the host vehicle in response to the determinednavigational action. For example, a brake may be applied in order togive way to vehicle 1703 in FIG. 17A, and an accelerator may be appliedalong with steering of the wheels of the host vehicle in order to causethe host vehicle to enter the roundabout behind vehicle 1703, as shownif FIG. 17B.

As described in the examples above, navigation of the host vehicle maybe based on the navigational characteristics of a target vehiclerelative to another vehicle or object. Additionally, navigation of thehost vehicle may be based on navigational characteristics of the targetvehicle alone without a particular reference to another vehicle orobject. For example, at step 1807 of FIG. 18 , analysis of a pluralityof images captured from an environment of a host vehicle may enabledetermination of at least one navigational characteristic of anidentified target vehicle indicative of a level of aggression associatedwith the target vehicle. The navigational characteristic may include avelocity, acceleration, etc. that need not be referenced with respect toanother object or target vehicle in order to make anaggressive/defensive determination. For example, observed accelerationsand/or velocities associated with a target vehicle that exceed apredetermined threshold or fall within or exceed a range of values mayindicate aggressive behavior. Conversely, observed accelerations and/orvelocities associated with a target vehicle that fall below apredetermined threshold or fall within or exceed a range of values mayindicate defensive behavior.

Of course, in some instances the observed navigational characteristic(e.g., a location, distance, acceleration, etc.) may be referencedrelative to the host vehicle in order to make the aggressive/defensivedetermination. For example, an observed navigational characteristic ofthe target vehicle indicative of a level of aggression associated withthe target vehicle may include an increase in relative accelerationbetween the target vehicle and the host vehicle, a following distance ofthe target vehicle behind the host vehicle, a relative velocity betweenthe target vehicle and the host vehicle, etc.

Navigation Based on Accident Liability Constraint

As described in the sections above, planned navigational actions may betested against predetermined constraints to ensure compliance withcertain rules. In some embodiments, this concept may be extended toconsiderations of potential accident liability. As discussed below, aprimary goal of autonomous navigation is safety. As absolute safety maybe impossible (e.g., at least because a particular host vehicle underautonomous control cannot control the other vehicles in itssurroundings—it can only control its own actions), the use of potentialaccident liability as a consideration in autonomous navigation and,indeed, as a constraint to planned actions may help ensure that aparticular autonomous vehicle does not take any actions that are deemedunsafe—e.g., those for which potential accident liability may attach tothe host vehicle. If the host vehicle takes only actions that are safeand that are determined not to result in an accident of the hostvehicle's own fault or responsibility, then desired levels of accidentavoidance (e.g., fewer than 10⁻⁹ per hour of driving) may be achieved.

The challenges posed by most current approaches to autonomous drivinginclude a lack of safety guarantees (or at least an inability to providedesired levels of safety), and also a lack of scalability. Consider theissue of guaranteeing multi-agent safe driving. As society will unlikelytolerate road accident fatalities caused by machines, an acceptablelevel of safety is paramount to the acceptance of autonomous vehicles.While a goal may be to provide zero accidents, this may be impossiblesince multiple agents are typically involved in an accident and one mayenvision situations where an accident occurs solely due to the blame ofother agents. For example, as shown in FIG. 19 , host vehicle 1901drives on a multi-lane highway, and while host vehicle 1901 can controlits own actions relative to the target vehicles 1903, 1905, 1907, and1909, it cannot control the actions of the target vehicles surroundingit. As a result, host vehicle 1901 may be unable to avoid an accidentwith at least one of the target vehicles should vehicle 1905, forexample, suddenly cut in to the host vehicle's lane on a collisioncourse with the host vehicle. To address this difficulty, a typicalresponse of autonomous vehicle practitioners is to resort to astatistical data-driven approach where safety validation becomes tighteras data over more mileage is collected.

To appreciate the problematic nature of a data-driven approach tosafety, however, consider first that the probability of a fatalitycaused by an accident per one hour of (human) driving is known to be10⁻⁶. It is reasonable to assume that for society to accept machines toreplace humans in the task of driving, the fatality rate should bereduced by three orders of magnitude, namely to a probability of 10⁻⁹per hour. This estimate is similar to the assumed fatality rate of airbags and from aviation standards. For example, 10⁻⁹ is the probabilitythat a wing will spontaneously detach from an aircraft in mid-air.Attempts to guarantee safety using a data-driven statistical approachthat provides additional confidence with accumulating miles driven,however, is not practical. The amount of data required to guarantee aprobability of 10⁻⁹ fatality per hour of driving is proportional to itsinverse (i.e., 10⁹ hours of data) which is roughly on the order ofthirty billion miles. Moreover, a multi-agent system interacts with itsenvironment and likely cannot be validated offline (unless a realisticsimulator emulating real human driving with all its richness andcomplexities such as reckless driving is available—but the problem ofvalidating the simulator would be even more difficult than creating asafe autonomous vehicle agent). And any change to the software ofplanning and control will require a new data collection of the samemagnitude, which is clearly unwieldy and impractical. Further,developing a system through data invariably suffers from lack ofinterpretability and explainability of the actions being taken—if anautonomous vehicle (AV) has an accident resulting in a fatality, we needto know the reason. Consequently, a model-based approach to safety isrequired, but the existing “functional safety” and ASIL requirements inthe automotive industry are not designed to cope with multi-agentenvironments.

A second primary challenge in developing a safe driving model forautonomous vehicles is the need for scalability. The premise underlyingAV goes beyond “building a better world” and instead is based on thepremise that mobility without a driver can be sustained at a lower costthan with a driver. This premise is invariably coupled with the notionof scalability—in the sense of supporting mass production of AVs (in themillions) and more importantly of supporting a negligible incrementalcost to enable driving in a new city. Therefore, the cost of computingand sensing does matter, if AV is to be mass manufactured, the cost ofvalidation and the ability to drive “everywhere” rather than in a selectfew cities is also a necessary requirement to sustain a business.

The issue with most current approaches lies in a “brute force” state ofmind along three axes: (i) the required “computing density,” (ii) theway high-definition maps are defined and created, and (iii) the requiredspecification from sensors. A brute-force approach goes againstscalability and shifts the weight towards a future in which unlimitedon-board computing is ubiquitous, where the cost of building andmaintaining HD-maps becomes negligible and scalable, and exotic superadvanced sensors would be developed, productized to automotive grade,and at a negligible cost. A future for which any of the above comes tofruition is indeed plausible but having all of the above hold is likelya low-probability event. Thus, there is a need to provide a formal modelthat pieces together safety and scalability into an AV program thatsociety can accept and is scalable in the sense of supporting millionsof cars driving anywhere in the developed countries.

The disclosed embodiments represent a solution that may provide thetarget levels of safety (or may even surpass safety targets) and mayalso be scalable to systems including millions of autonomous vehicles(or more). On the safety front, a model called “Responsibility-SensitiveSafety” (RSS) is introduced that formalizes the notion of “accidentblame,” is interpretable and explainable, and incorporates a sense of“responsibility” into the actions of a robotic agent. The definition ofRSS is agnostic to the manner in which it is implemented—which is a keyfeature to facilitate a goal of creating a convincing global safetymodel. RSS is motivated by the observation (as in FIG. 19 ) that agentsplay a non-symmetrical role in an accident where typically only one ofthe agents is responsible for the accident and therefore is to beresponsible for it. The RSS model also includes a formal treatment of“cautious driving” under limited sensing conditions where not all agentsare always visible (due to occlusions, for example). One primary goal ofthe RSS model is to guarantee that an agent will never make an accidentof its “blame” or for which it is responsible. A model may be usefulonly if it comes with an efficient policy (e.g., a function that mapsthe “sensing state” to an action) that complies with RSS. For example,an action that appears innocent at the current moment might lead to acatastrophic event in the far future (“butterfly effect”). RSS may beuseful for constructing a set of local constraints on the short-termfuture that may guarantee (or at least virtually guarantee) that noaccidents will happen in the future as a result of the host vehicle'sactions.

Another contribution evolves around the introduction of a “semantic”language that consists of units, measurements, and action space, andspecification as to how they are incorporated into planning, sensing andactuation of the AV. To get a sense of semantics, in this context,consider how a human taking driving lessons is instructed to think abouta “driving policy.” These instructions are not geometric—they do nottake the form “drive 13.7 meters at the current speed and thenaccelerate at a rate of 0.8 m/s²”. Instead, the instructions are of asemantic nature—“follow the car in front of you” or “overtake that caron your left.” The typical language of human driving policy is aboutlongitudinal and lateral goals rather than through geometric units ofacceleration vectors. A formal semantic language may be useful onmultiple fronts connected to the computational complexity of planningthat do not scale up exponentially with time and number of agents, tothe manner in which safety and comfort interact, to the way thecomputation of sensing is defined and the specification of sensormodalities and how they interact in a fusion methodology. A fusionmethodology (based on the semantic language) may ensure that the RSSmodel achieves the required 10⁻⁹ probability of fatality, per one hourof driving, all while performing only offline validation over a datasetof the order of 10⁵ hours of driving data.

For example, in a reinforcement learning setting, a Q function (e.g., afunction evaluating the long term quality of performing an action aϵAwhen the agent is at state sϵS; given such a Q-function, a naturalchoice of an action may be to pick the one with highest quality,π(s)=argmax_(a) Q(s, a)) may be defined over a semantic space in whichthe number of trajectories to be inspected at any given time is boundedby 10⁴ regardless of the time horizon used for planning. The signal tonoise ratio in this space may be high, allowing for effective machinelearning approaches to succeed in modeling the Q function. In the caseof computation of sensing, semantics may allow for distinguishingbetween mistakes that affect safety versus those mistakes that affectthe comfort of driving. We define a PAC model (Probably ApproximateCorrect (PAC)), borrowing Valiants PAC-learning terminology) for sensingwhich is tied to the Q-function and show how measurement mistakes areincorporated into planning in a manner that complies with RSS yet allowsfor optimization of the comfort of driving. The language of semanticsmay be important for the success of certain aspects of this model asother standard measures of error, such as error with respect to a globalcoordinate system, may not comply with the PAC sensing model. Inaddition, the semantic language may be an important enabler for definingHD-maps that can be constructed using low-bandwidth sensing data andthus be constructed through crowd-sourcing and support scalability.

To summarize, the disclosed embodiments may include a formal model thatcovers important ingredients of an AV: sense, plan, and act. The modelmay help ensure that from a planning perspective there will be noaccident of the AV's own responsibility. And also through a PAC-sensingmodel, even with sensing errors, the described fusion methodology mayrequire only offline data collection of a very reasonable magnitude tocomply with the described safety model. Furthermore, the model may tietogether safety and scalability through the language of semantics,thereby providing a complete methodology for a safe and scalable AV.Finally, it is worth noting that developing an accepted safety modelthat would be adopted by the industry and regulatory bodies may be anecessary condition for the success of AV.

The RSS model may generally follow a classic sense-plan-act roboticcontrol methodology. The sensing system may be responsible forunderstanding a present state of the environment of a host vehicle. Theplanning part, which may be referred to as a “driving policy” and whichmay be implemented by a set of hard-coded instructions, through atrained system (e.g., a neural network), or a combination, may beresponsible for determining what is the best next move in view ofavailable options for accomplishing a driving goal (e.g., how to movefrom the left lane to a right lane in order to exit a highway). Theacting portion is responsible for implementing the plan (e.g., thesystem of actuators and one or more controllers for steering,accelerating, and/or braking, etc. a vehicle in order to implement aselected navigational action). The described embodiments below focusprimarily on the sensing and planning parts.

Accidents may stem from sensing errors or planning errors. Planning is amulti-agent endeavor, as there are other road users (humans andmachines) that react to actions of an AV. The described RSS model isdesigned to address safety for the planning part, among others. This maybe referred to as multi-agent safety. In a statistical approach,estimation of the probability of planning errors may be done “online.”Namely, after every update of the software, billions of miles must bedriven with the new version to provide an acceptable level of estimationof the frequency of planning errors. This is clearly infeasible. As analternative, the RSS model may provide a 100% guarantee (or virtually100% guarantee) that the planning module will not make mistakes of theAV's blame (the notion of “blame” is formally defined). The RSS modelmay also provide an efficient means for its validation not reliant upononline testing.

Errors in a sensing system may be easier to validate, because sensingcan be independent of the vehicle actions, and therefore we can validatethe probability of a severe sensing error using “offline” data. But,even collecting offline data of more than 109 hours of driving ischallenging. As part of the description of a disclosed sensing system, afusion approach is described that can be validated using a significantlysmaller amount of data.

The described RSS system may also be scalable to millions of cars. Forexample, the described semantic driving policy and applied safetyconstraints may be consistent with sensing and mapping requirements thatcan scale to millions of cars even in today's technology.

A foundational building block of such a system is a thorough safetydefinition, that is, a minimal standard to which AV systems may need toabide. In the following technical lemma, a statistical approach tovalidation of an AV system is shown to be infeasible, even forvalidating a simple claim such as “the system makes N accidents perhour”. This implies that a model-based safety definition is the onlyfeasible tool for validating an AV system.

Lemma 1 Let X be a probability space, and A be an event for whichPr(A)=p₁<0.1. Assume we sample

$m = \frac{1}{p_{1}}$i.i.d. samples from X, and let Z=Σ_(i=1) ^(m) 1_([x∈A]). ThenPr(Z=0)≥e ⁻².Proof We use the inequality 1−x≥e^(−2x) (proven for completeness inAppendix A.1), to getPr(Z=0)=(1−p ₁)^(m) ≥e ^(−2p) ¹ ^(m) =e ⁻².Corollary 1 Assume an AV system AV makes an accident with small yetinsufficient probability p₁. Any deterministic validation procedurewhich is given 1/p₁ samples, will, with constant probability, notdistinguish between AV₁ and a different AV system AV₀ which never makesaccidents.

To gain perspective over the typical values for such probabilities,assume we desire an accident probability of 10⁻⁹ per hour, and a certainAV system provides only 10⁻⁸ probability. Even if the system obtains 10⁸hours of driving, there is constant probability that the validationprocess will not be able to indicate that the system is dangerous.

Finally, note that this difficulty is for invalidating a single,specific, dangerous AV system. A full solution cannot be a viewed as asingle system, as new versions, bug fixes, and updates will benecessary. Each change, even of a single line of code, generates a newsystem from a validator's perspective. Thus, a solution which isvalidated statistically, must do so online, over new samples after everysmall fix or change, to account for the shift in the distribution ofstates observed and arrived-at by the new system. Repeatedly andsystematically obtaining such a huge number of samples (and even then,with constant probability, failing to validate the system), isinfeasible.

Further, any statistical claim must be formalized to be measured.Claiming a statistical property over the number of accidents a systemmakes is significantly weaker than claiming “it drives in a safemanner.” In order to say that, one must formally define what is safety.

Absolute Safety is Impossible

An action a taken by a car c may be deemed absolutely safe if noaccident can follow the action at some future time. It can be seen thatit is impossible to achieve absolute safety, by observing simple drivingscenarios, for example, as depicted in FIG. 19 . From the perspective ofvehicle 1901, no action can ensure that none of the surrounding carswill crash into it. Solving this problem by forbidding the autonomouscar from being in such situations is also impossible. As every highwaywith more than two lanes will lead to it at some point, forbidding thisscenario amounts to a requirement to remain in the garage. Theimplications might seem, at first glance, disappointing. Nothing isabsolutely safe. However, such a requirement for absolute safety, asdefined above, may be too harsh, as evident by the fact that humandrivers do not adhere to a requirement for absolute safety. Instead,humans behave according to a safety notion that depends onresponsibility.

Responsibility-Sensitive Safety (RSS)

An important aspect missing from the absolute safety concept is thenon-symmetry of most accidents—it is usually one of the drivers who isresponsible for a crash, and is to be blamed. In the example of FIG. 19, the central car 1901 is not to be blamed if the left car 1909, forexample, suddenly drives into it. To formalize the fact that consideringits lack of responsibility, a behavior of AV 1901 staying in its ownlane can be considered safe. To do so, a formal concept of “accidentblame” or accident responsibility, which can serve as the premise for asafe driving approach, is described.

As an example, consider the simple case of two cars c_(f), c_(r),driving at the same speed, one behind the other, along a straight road.Assume c_(f), the car at the front, suddenly brakes because of anobstacle appearing on the road, and manages to avoid it. Unfortunately,c_(r) did not keep enough of a distance from c_(f), is not able torespond in time, and crashes into c_(f)'s rear side. It is clear thatthe blame is on c_(r); it is the responsibility of the rear car to keepsafe distance from the front car, and to be ready for unexpected, yetreasonable, braking.

Next, consider a much broader family of scenarios: driving in amulti-lane road, where cars can freely change lanes, cut into othercars' paths, drive at different speeds, and so on. To simplify thefollowing discussion, assume a straight road on a planar surface, wherethe lateral, longitudinal axes are the x, y axes, respectively. This canbe achieved, under mild conditions, by defining a homomorphism betweenthe actual curved road and a straight road. Additionally, consider adiscrete time space. Definitions may aid in distinction between twointuitively different sets of cases: simple ones, where no significantlateral maneuver is performed, and more complex ones, involving lateralmovement.

Definition 1 (Car Corridor) The corridor of a car c is the range[c_(x,left),c_(x,right)]×[±∞], where c_(x,left),c_(x,right) are thepositions of the leftmost, rightmost corners of c.

Definition 2 (Cut-in) A car c₁ (e.g., car 2003 in FIGS. 20A and 20B)cuts-in to car c₀'s (e.g., car 2001 in FIGS. 20A and 20B) corridor attime t if it did not intersect c₀'s corridor at time t−1, and doesintersect it at time t.

A further distinction may be made between front/back parts of thecorridor. The term “the direction of a cut-in” may describe movement inthe direction of the relevant corridor boundary. These definitions maydefine cases with lateral movement. For the simple case where there isno such occurrence, such as the simple case of a car following another,the safe longitudinal distance is defined:

Definition 3 (Safe longitudinal distance) A longitudinal distance 2101(FIG. 21 ) between a car c_(r) (car 2103) and another car c_(f) (car2105) that is in c_(r)'s frontal corridor is safe w.r.t. a response timep if for any braking command a, |a|<a_(max,brake), performed by c_(f),if c_(r) will apply its maximal brake from time p until a full stop thenit won't collide with c_(f).

Lemma 2 below calculates d as a function of the velocities of c_(r),c_(f), the response time ρ, and the maximal acceleration a_(max,brkae).Both ρ and a_(max,brake) are constants, which should be determined tosome reasonable values by regulation. In further examples, either one ofresponse time ρ and the maximal acceleration a_(max,brake) may be setfor a specific vehicle or vehicle type, or may be adapted/adjustedaccording to measurements or otherwise input parameters regarding thevehicle condition, the road condition, the user's (e.g., a driver or apassenger) preferences, etc.

Lemma 2 Let c_(r) be a vehicle which is behind c_(f) on the longitudinalaxis. Let a_(max,brake), a_(max,accel) be the maximal braking andacceleration commands, and let ρ be c_(r)'s response time. Let υ_(r),υ_(f) be the longitudinal velocities of the cars, and let l_(f), l_(r)be their lengths. Define υ_(p,max)=υ_(r)+ρ·a_(max,accel), and define

$T_{r} = {{p + {\frac{v_{p,\max}}{a_{\max,{brake}}}\mspace{14mu}{and}\mspace{14mu} T_{f}}} = {\frac{v_{f}}{a_{\max,{brake}}}.}}$Let L=(l_(r)+l_(f))/2. Then, the minimal safe longitudinal distance forc_(r) is:

$d_{\min} = \{ \begin{matrix}L & {{{if}\mspace{20mu} T_{r}} \leq T_{f}} \\\begin{matrix}{L + {T_{f}\lbrack {( {v_{p,\max} - v_{f}} ) + {\rho\; a_{\max,{brake}}}} \rbrack} -} \\{\frac{\rho^{2}a_{\max,{brake}}}{2} + \frac{( {T_{r} - T_{f}} )( {v_{p,\max} - {( {T_{f} - \rho} )a_{\max,{brake}}}} )}{2}}\end{matrix} & {otherwise}\end{matrix} $

Proof Let d_(t) be the distance at time t. To prevent an accident, wemust have that d_(t)>L for every t. To construct d_(min) we need to findthe tightest needed lower bound on d₀. Clearly, d₀ must be at least L.As long as the two cars didn't stop after T≥ρ seconds, the velocity ofthe preceding car will be υ_(f)−T a_(max,brake) while c_(r)'s velocitywill be upper bounded by υ_(p,max)−(T−ρ) a_(max,accel). So, the distancebetween the cars after T seconds will be lower bounded by:

$d_{T}:={d_{0} + {\frac{T}{2}( {{2v_{f}} - {T\mspace{11mu} a_{\max,{brake}}}} )} - {\quad{\lbrack {{\rho\; v_{\rho,\max}} + {\frac{T - \rho}{2}( {{2v_{\rho,\max}} - {( {T - \rho} )a_{\max,{brake}}}} )}} \rbrack = {d_{0} + {T\lbrack {( {v_{f} - v_{\rho,\max}} ) - {\rho\; a_{\max,{brake}}}} \rbrack} + \frac{\rho^{2}a_{\max,{brake}}}{2}}}}}$

Note that T_(r) is the time on which c_(r) arrives to a full stop (avelocity of 0) and T_(f) is the time on which the other vehicle arrivesto a full stop. Note that a_(max,brake)(T_(r)-T_(f))=υ_(ρ,max)−υ_(f)+ρa_(max,brake), so if T_(r)≤T_(f) ifsuffices to require that d₀<L. If T_(r)<T_(f) then

$d_{T_{r}} = {d_{0} + {T_{f}\lbrack {( {v_{f} - v_{\rho,\max}} ) - {\rho\; a_{\max,{brake}}}} \rbrack} + \frac{\rho^{2}a_{\max,{brake}}}{2} - {\frac{( {T_{r} - T_{f}} )( {v_{\rho,\max} - {( {T_{f} - \rho} )a_{\max,{brake}}}} )}{2}.}}$Requiring d_(Tr)>L and rearranging terms concludes the proof.

Finally, a comparison operator is defined which allows comparisons withsome notion of “margin”: when comparing lengths, velocities and so on,it is necessary to accept very similar quantities as “equal”.

Definition 4 (μ-comparison) The μ-comparison of two numbers a, b isa>_(μ) b if a>b+μ, a<_(μ) b if a<b−μ and a=_(μ)b I f|a−b|≤μ.

The comparisons (argmin, argmax, etc.) below are μ-comparisons for somesuitable μs. Assume an accident occurred between cars c₁, c₂. Toconsider who is to blame for the accident, the relevant moment whichneeds to be examined is defined. This is some point in time whichpreceded the accident, and intuitively, was the “point of no return”;after it, nothing could be done to prevent the accident.

Definition 5 (Blame Time) The Blame Time of an accident is the earliesttime preceding the accident in which:

there was an intersection between one of the cars and the other'scorridor, and

the longitudinal distance was not safe.

Clearly there is such a time, since at the moment of accident, bothconditions hold. Blame Times may be split into two separate categories:

-   -   Ones in which a cut-in also occurs, namely, they are the first        moment of intersection of one car and the other's corridor, and        it's in a non-safe distance.    -   Ones in which a cut-in does not occur, namely, there was        intersection with the corridor already, in a safe longitudinal        distance, and the distance had changed to unsafe at the Blame        Time.

Definition 6 (μ-Losing by Lateral Velocity) Assume a cut-in occursbetween cars c₁, c₂. We say that c₁ μ-Loses by Lateral Velocity in caseits lateral velocity w.r.t. the direction of the cut-in is higher by μthan that of c₂.

It should be noted that the direction of the velocity is important: Forexample, velocities of −1, 1 (both cars crashing into each other) is atie, however if the velocities are 1, 1+μ/2, the one with positivedirection towards the other car is to be blamed. Intuitively, thisdefinition will allow us to blame a car which drives laterally very fastinto another.

Definition 7 (μ₁, μ₂)-Winning by Lateral Position) Assume a cut-inoccurs between cars c₁, c₂. We say that c₁ (μ₁, μ₂)-Wins by LateralPosition in case its lateral position w.r.t. the cut-in lane's center(the center closest to the cut-in relevant corridor) is smaller than μ₁(in absolute value), and smaller by μ₂ than that of c₂.

Intuitively, we will not blame a car if it's very close to the lanecenter (μ₁), and much closer than the other car (by μ₂).

Definition 8 (Blame) The Blame or responsibility for an accident betweencars c₁, c₂, is a function of the state at the Blame Time, and isdefined as follows:

-   -   If the Blame Time is not a cut-in time, the blame is on the rear        car.    -   If the Blame Time is also a cut-in time, the blame is on both        cars, unless for one of the cars, w.l.o.g. c₁, the two following        conditions hold, for some predefined μs:        -   It doesn't lose by Lateral Velocity,        -   It wins by Lateral Position.

In that case, c1 is spared. In other words, if an unsafe cut-in occurs,both cars are to blame, unless one of the cars is not (significantly)laterally faster, and is (significantly) closer to the lane center. Bythis, the desired behavior is captured: if following a car, keep a safedistance, and if cutting into a corridor of a car which simply drives inits own lane, do it only at a safe distance. An automatedcontroller-based system for following the safety guidelines describedabove should not lead to overly defensive driving, as discussed furtherbelow.

Dealing with Limited Sensing

After considering the highway example, a second example next addresses aproblem of limited sensing. A very common human response, when blamedfor an accident, falls into the “but I couldn't see him” category. Itis, many times, true. Human sensing capabilities are limited, sometimesbecause of an unaware decision to focus on a different part of the road,sometimes because of carelessness, and sometimes because of physicallimitations—it is impossible to see a pedestrian hidden behind a parkedcar. Of those human limitations, advanced automatic sensing systems mayonly be subject to the latter: 360° view of the road, along with thefact that computers are never careless, puts them above human sensingcapabilities. Returning to the “but I couldn't see him” example, afitting answer is “well, you should've been more careful.” To formalizewhat is being careful with respect to limited sensing, consider thescenario, depicted in FIG. 22 . Car 2201 (c₀) is trying to exit aparking lot, merging into a (possibly) busy road, but cannot see whetherthere are cars in the street because its view is obscured by building2203. Assume that this is an urban, narrow street, with a speed limit of30 km/h. A human driver's behavior is to slowly merge onto the road,obtaining more and more field of view, until sensing limitations areeliminated. A significant moment in time should be defined—the firsttime the occluded object is exposed to us; after its exposure, one dealwith it just like any other object that one can sense.

Definition 9 (Exposure Time) The Exposure Time of an object is the firsttime in which we see it.

Definition 10 (Blame due to Unreasonable Speed) Assume that at theexposure time or after it, car c₁ (car 2205) was driving at speedυ>υ_(limit), and c₀ wasn't doing so. Then, the blame is only on c₁. Wesay that c₁ is blamed due to unreasonable speed.

This extension allows c₀ to exit the parking lot safely. Using ourprevious responsibility-sensitive safety definitions, along with adynamic υ_(limit) definition (which uses the road conditions and speedlimit, plus reasonable margins), the only necessity is to check whetherin the worst case, as illustrated in the figure, the cut-in is in a safelongitudinal distance, while assuming that c₁ will not exceed υ_(limit).Intuitively, this encourages c₀ to drive slower and further from theoccluder, thus slowly increasing its field of view and later allowingfor safe merging into the street.

Having extended the accident responsibility definition to this basiccase of limited sensing, a family of extensions may address similarcases. Simple assumptions as to what can be occluded (a potentially fastcar cannot be occluded between two closely parked cars, but a pedestriancan), and what is the worst case maneuver it can perform (a pedestrian'sυ_(limit) is much smaller than that of a car), imply restrictions ondriving—one must be prepared for the worst, and have the ability torespond if suddenly, the exposure time comes. A more elaborate example,in an urban scenario, can be taken from the scenario of a pedestrianwhich is possibly occluded by a parked car. Accident blame for accidentswith a pedestrian may be defined:

Definition 11 (Accident-with-Pedestrian Blame) TheAccident-with-Pedestrian Blame is always on the car, unless one of thefollowing three holds:

-   -   the car hits the pedestrian with the car's side, and the lateral        velocity of the car is smaller than μ, w.r.t. the direction of        the hit.    -   the pedestrian's velocity at the exposure time or later was        larger than υ_(limit).    -   the car is at complete stop.

Informally, the car is not to blame only if a pedestrian runs into itsside, while the car does not ride faster than μ into the pedestrian, orif the car is at stop, or if the pedestrian was running super-humanlyfast, in some direction, not necessarily the hitting direction.

While the described system may not ensure absolute safety, it may leadto a scenario where very few (if any) accidents occur among autonomousvehicles. For example, where all cars (and other road users) are able tosuccessfully verify that they will not be blamed for an accident as aresult of an action taken, accidents may be eliminated. By definition,for every accident there is at least one responsible car. Thus, if nocar takes an action for which it may be responsible for a resultingaccident (according to the RSS model described above), there shouldnever be any accidents, leading to the type of absolute safety or nearabsolute safety sought by unwieldy and impractical statistical methods.

Not all roads are of a simple structure. Some, like junctions androundabouts, contain more complex situations, along with various rightof way rules. Not all occluded objects are cars or pedestrians, withbicycles and motorcycles all legitimate road users to be considered. Theprinciples introduced in this section may be extended to theseadditional cases.

Efficiently Validated Conditions for Responsibility-Sensitive Safety

This section discusses implementation aspects of RSS. To begin, itshould be noted that an action that is performed now may have abutterfly effect that will lead to a chain of events with an accidentafter 10 minutes of driving, for example. A “brute-force” approach ofchecking all possible future outcomes not only impractical, it is likelyimpossible. To overcome this challenge, the responsibility-sensitivesafety definitions described above are now described together withcomputationally efficient methods to validate them.

Computationally Feasible Safety Verification.

The main mathematical tool for computationally feasible verification is“induction.” To prove a claim by induction, one begins with proving theclaim for simple cases, and then, each induction step extends the proofto more and more involved cases. To illustrate how this induction toolcan be helpful for safety verification, consider again the simpleexample of a car c_(r) following another, c_(f) (FIG. 21 ). Thefollowing constraint may be applied on the policy of c_(r). At each timestep t, the policy can pick any acceleration command such that even ifc_(f) will apply a deceleration of −a_(max), the resulting distancebetween c_(r) and c_(f) at the next time step will be at least the safelongitudinal distance (defined in Definition 3 and Lemma 2). If no suchaction exists, c_(r) must apply the deceleration −a_(max). The followinglemma uses induction to prove that any policy that adheres to the aboveconstraints will never make an accident with cf.

Lemma 3 Under the assumptions given in Definition 3, if the policy ofc_(r) adheres to the constraints given above it will never make anaccident with cf.

Proof The proof is by induction. For the induction base, start with aninitial state in which the distance between the two cars is safe(according to Lemma 2). The induction step is as follows. Consider thedistance between c_(r) and c_(f) at some time t. If there is an actionthat results in a safe distance (even with c_(f) making maximaldeceleration), we are fine. If all actions cannot guarantee safedistance, let t′<t be the maximal time in which we took an action whichwas not maximal deceleration. By the induction hypothesis, at time t′+1,we were in a safe distance, and from there on we performed maximaldeceleration. Hence, by the definition of safe distance, there was nocrash from time t′ till now, which concludes the proof.

The above example demonstrates a more general idea: there's someemergency maneuver which can be performed by c_(r) in an extreme case,and lead it back to a “safe state.” It should be noted that theconstraints on the policy we have described above depend on just onefuture time step, hence it can be verified in a computationallyefficient manner.

To generalize those ideas of sufficient local properties for RSS, wefirstly define a Default Emergency Policy (DEP), and use it as abuilding block for defining a local property of action-taking which wecall “cautious”. It is then shown that taking only cautious commands issufficient for RSS.

Definition 12 (Default Emergency Policy) The Default Emergency Policy(DEP) is to apply maximum braking power, and maximum heading changetowards 0 heading w.r.t. the lane. The maximum braking power and headingchange are derived from physical parameters of the car (and maybe alsofrom weather and road conditions). Definition 13 (Safe state) A state sis safe if performing DEP starting from it will not lead to an accidentof our blame. As in the simple case of a car following another, wedefine a command to be cautious if it leads to a safe state. Definition14 (Cautious command) Suppose we are currently at state so. A command ais cautious if the next state, s₁, will be safe with respect to a set Aof possible commands that other vehicles might perform now. The abovedefinition depends on the worst-case commands, in the set A, othervehicles might perform. We will construct the set A based on reasonableupper bounds on maximum braking/acceleration and lateral movements.

The following theorem proves, by induction again, that if we only issuecautious commands then there will be no accidents of our blame. Theorem1 Assume that in time 0, c is in a safe state, and for every time step,c only issues cautious commands, where if no cautious command exists atsome time step, c applies DEP. Then, c will never make accidents of itsblame. Proof By induction. The base of the induction follows from thedefinition of a safe state and step from the definition of a cautiouscommand.

One benefit of this approach is that there may be no need to checkinfinite future, as we can quickly return to a safe state, and continuesafely from there. Moreover, given the fact we will plan again at t+1,and hence be able to perform DEP then if necessary, we should only checkthe command we are giving at time t, and not a possible longer plan wemight have in mind—we can change that plan at t+1. Now, incorporating alearning component in a system, when it is verified at run time by thistransparent model, is made possible. Finally, this local verificationimplies full future RSS, which is our desired goal. An implementationobstacle is that the cautiousness definition involves all trajectoriesanother agent can perform until t_(brake), which, even for moderatet_(brake), is a huge space. To tackle this, we next turn to develop anefficiently computable way to verify cautiousness, and hence RSS, in ascalable manner.

Efficient Cautiousness Verification

A first observation is that a state is not safe if and only if thereexists a specific vehicle, {tilde over (c)}, which can perform commandsfrom the set A which lead to an accident of our blame while we executethe DEP. Therefore, in a scene with a single target car, denoted {tildeover (c)}, and in the general case, the procedure may be executedsequentially, for each of the other vehicles in the scene.

When considering a single target car, an action a is not cautious if andonly if there is a sequence of commands for {tilde over (c)}, denotedã₁, . . . , ãt_(brake), all in the set A, that results in an accident ofc's blame. As already proven, if at time 0, it holds that {tilde over(c)} is in the frontal corridor of c, there is a simple way to check thecautiousness of a—we just need to verify that even if {tilde over (c)}will apply maximal brake for one time step (and we'll perform a), theresulting longitudinal distance will remain safe. The lemma below givesa sufficient condition for cautiousness in the more involved cases,where lateral maneuvers are to be considered too.

Lemma 4 Assume that at time T=0, {tilde over (c)} is not in the frontalcorridor of c. Then, if at every T∈(0, t_(brake)], there is no non-safecut in of c's blame, then a is cautious.

Proof Suppose that a is not cautious, namely, there exists ã₁, . . . ,ãt_(brake) that leads to an accident of c's blame. Before the accidentthere must be a cut-in time, T. Assume first that T>0. If this cut-inwas at a safe longitudinal distance, then there cannot be an accident ofour blame due to the fact that DEP is executed by deceleration of−a_(max) and based on the definition of safe longitudinal distance (andwe assume here that the response time ρ is larger than the timeresolution of steps). If the cut-in was non-safe, by the assumption ofthe lemma it was not of c's blame, hence the accident is also not of c'sblame.

Finally, if T<0, by the assumption of the lemma, at the moment ofcutting, {tilde over (c)} was at the back corridor of c. By induction, cperformed only safe cut-ins in the past, and hence either the cut-in wassafe or it was c's blame. In both cases, the current accident is not ofc's blame.

In light of Lemma 4, the problem of checking whether there can be anon-safe cut in of c's blame remains. An efficient algorithm ispresented below for checking the possibility of a non-safe cut-in attime t. To validate the entire trajectory we discretize the timeinterval [0, t_(brake)] and apply the algorithm on all time intervals(with a slightly larger value of p in the definition of safe distance toensure that the discretization doesn't hurt). Let {tilde over(c)}_(diag) be the length of a diagonal of a minimal rectangle bounding{tilde over (c)}. For each time t∈[0, t_(brake)], define c_(length)(t)to be the longitudinal “span” of c in time t, and let

${L(t)} = {\frac{{\overset{\sim}{c}}_{diag} + c_{{length}{\lbrack t\rbrack}}}{2}.}$Define c_(width)[t] in similar fashion and

${W(t)} = {\frac{{\overset{\sim}{c}}_{diag} + c_{{width}{\lbrack t\rbrack}}}{2}.}$

Algorithm 1: Check the possibility of a non-safe cut-in at time t input:{tilde over (y)}[0], {tilde over (v)}_(y)[0], {tilde over (x)}[0],{tilde over (v)}_(x)[0] are longitudinal/lateral position/velocity of{tilde over (c)} at time 0 y[t], v_(y)[t], x[t], v_(x)[t] arelongitudinal/lateral position/velocity of c at time t a_(y, min),a_(y, max), are longitudinal acceleration boundaries a_(x, max) is alateral acceleration absolute value boundary L = L(t), W = W(t) checklongitudinal feasibility: let {tilde over (y)}_(min) = {tilde over(y)}[0] + {tilde over (v)}_(y)[0]t + ½a_(y, min)t² let {tilde over(y)}_(max) = {tilde over (y)}[0] + {tilde over (v)}_(y)[0]t +½a_(y, max)t² if [{tilde over (y)}_(min), {tilde over (y)}_(max)] ∩[y[t] − L, y[t] + L] ≠ ∅ continue to check lateral feasibility else if{tilde over (y)}_(min) > y[t] + L and ({tilde over (y)}_(min), {tildeover (v)}_(y)[0] + a_(y, min)t) is not longitudinally safe w.r.t. (y[t],v_(y)[t]) continue to check lateral feasibility else if {tilde over(y)}_(max) < y[t] − L and ({tilde over (y)}_(max), {tilde over(v)}_(y)[0] + a_(y, max)t) is not longitudinally safe w.r.t. (y[t],v_(y)[t]) continue to check lateral feasibility return “non-feasible”check lateral feasibility: w.l.o.g. assume x[t] = 0 and {tilde over(x)}[0] ≤ 0, and {tilde over (v)}_(x)[0] ≥ 0. if a position x[t] is notconsidered (μ₁, μ₂)-Winning by Lateral Position w.r.t. a position x[t] -W w.l.o.g. assume v_(x)[t] = −μ, as in Definition 6. else w.l.o.g.assume v_(x)[t] = −2μ, as in Definition 6. let t_(top) = 0.5(t − {tildeover (v)}_(x)[0]/a_(x, max)) if t_(top) < 0 return “non-feasible” letx_(max) = {tilde over (x)}[0] + 2({tilde over (v)}[0]t_(top) +0.5a_(x, max)t_(top) ²) + {tilde over (v)}_(x)[0]²/(2a_(x, max)) ifx_(max) < −W return “non-feasible” return “feasible”

The following theorem proves the correctness of the above algorithm.

Theorem 2 If Algorithm 1 returns “non-feasible” then there cannot be anon-safe cut-in of the ego vehicle's blame at time t. To prove thetheorem, we rely on the following key lemmas, which prove thecorrectness of the two building blocks of Algorithm 1. Start with thelongitudinal feasibility:

Lemma 5 Under the notation of Algorithm 1, if the check longitudinalfeasibility procedure is concluded by returning “‘non-feasible”, thenthere cannot be anon-safe cut-in of the ego vehicle's blame at time t.

Proof Ignoring the lateral aspect of a cut-in maneuver, we examine themere possibility that the longitudinal distance between c and {tildeover (c)} will be unsafe. Itis clear that the positions ({tilde over(y)}_(min), {tilde over (y)}_(max)) are bounding the position which canbe attained by {tilde over (c)} at time t. By the fact [{tilde over(y)}_(min), {tilde over (y)}_(max)]∩[y[t]−L, y[t]+L]=ø, we obtain thatany longitudinally non-safe distance which is attainable, is ≥L. Assume{tilde over (y)}_(min)>y[t]+L, and assume by contradiction that anon-safe longitudinal position and velocity, denoted {tilde over(y)}_(bad)[t], {tilde over (υ)}_(ybad)[t], are attainable usingacceleration commands bounded by a_(y,min), a_(y,max). By definition of{tilde over (y)}_(min), we have {tilde over (y)}_(bad)[t]>{tilde over(y)}_(min), and hence the distance between the cars is larger, namely{tilde over (y)}_(bad)[t]−(y[t]+L)>{tilde over (y)}_(min)−(y[t]+L).Since ({tilde over (y)}_(min),{tilde over (υ)}_(y)[0]+a_(y,min)t) islongitudinally safe w.r.t. (y[t], υ_(y)[t]), by definition oflongitudinal non-safety, it follows that the attained velocity {tildeover (υ)}_(ybad)[t] must be smaller than {tilde over(υ)}_(y)[0]+a_(y,min)t. However, it is clear that in order to achievelesser speed, {tilde over (c)} must use average acceleration which islesser than a_(y,min) throughout the time window [0, t], thuscontradicting the fact that the longitudinal non-safety was attainedusing commands bounded by a_(y,min), a_(y,max). By considering asymmetrical argument for the case {tilde over (y)}_(max)<y[t]−L, theproof is completed.

Next, the lateral feasibility.

Lemma 6 Under the notation of Algorithm 1, if the check lateralfeasibility procedure is concluded by returning “non-feasible”, thenthere cannot be a non-safe cut-in of the ego vehicle's blame at time t.

Proof First, it is clear that there is no loss of generality by theassumptions x[t]=0, {tilde over (x)}[0]≤0 and the ones regardingv_(x)[t], by a simple change of coordinates and consideration ofrelative velocity. Moreover, by similar arguments it is simple to extendto the case when {tilde over (υ)}_(x)[0]≤0.

Note that the positions of the cars involved in the cut-in, which in ourcase, are (x[t], x[t]−W), imply some (μ1, μ2)-Winning by LateralPosition property, affecting the blame. By our assumptions overv_(x)[t], we obtain that the maximal lateral velocity {tilde over (c)}may use at time t, under assumption that c will be blamed, is 0: eitherin order to μ-“tie” lateral velocity (in the case c does not (μ1,μ2)-Winby Lateral Position, this can be enough in order to put the blame onit), or to μ-Win lateral velocity (in the case c does (μ1, μ2)-Win byLateral Position, this is necessary in order to put the blame on it). Itis left to check whether exists a maneuver starting at {tilde over(v)}_(x)[0], ending at {tilde over (υ)}_(x)[t]=0, using lateralaccelerations bounded by a_(x,max), with final position {tilde over(x)}[t]≥x[t]−W. In words, a cut-in which ends at the desired lateralvelocity, 0.

Recall the definition t_(op)=0.5(t−{tilde over (υ)}_(x)[0]/a_(x,max))from the algorithm. Assume t_(top)<0. This implies that the time neededby {tilde over (c)} in order to reach lateral velocity 0 when usingmaximal lateral acceleration, namely, {tilde over (υ)}_(x)[0]/a_(x,max),is lesser than t. This implies that there is no manoeuvre which it canperform in order to reach the desired velocity in time, and hence noproblematic maneuver exists. Therefore, if the procedure returned“non-feasible” due to t_(top)<0, indeed, there is no feasibility of anon-safe cut-in of c's blame.

Consider the case t_(top)>0. Then, the procedure returned “non-feasible”due to x_(max)<−W. Consider a family of lateral velocity profiles for{tilde over (c)} in the time range [0, t], denoted U={u_(a): a>{tildeover (v)}_(x)[0]/} and parameterized by a. We define, for each a, insimilar fashion to the one used in the algorithm,t_(top)(a):=0.5(t−{tilde over (υ)}_(x)[0]/a). Note that t_(top)(a)>0 forall a>{tilde over (υ)}_(x)[0]/t. We now define the velocity profileu_(a) for all times t′0 [0, t] as follows:

${u_{a}( t^{\prime} )} = \{ \begin{matrix}{{{\overset{˜}{\nu}}_{x}\lbrack 0\rbrack} + {a \cdot t^{t}}} & {t^{\prime} < {t_{top}(a)}} \\{{{\overset{˜}{v}}_{x}\lbrack 0\rbrack} + {a \cdot ( {{2{t_{top}(a)}} - t^{\prime}} )}} & {t^{\prime} \geq {t_{top}(a)}}\end{matrix} $

First, it can be seen that u_(a) satisfies the constraintsu_(a)(0)={tilde over (υ)}_(x)[0], u_(a)(t)={tilde over (υ)}_(x)[t].Second, the distance travelled while using u_(a) can be calculated, asthis amounts to integration of a piecewise linear function. Define thearrived-at position as {tilde over (x)}_(u) _(a) , and note that x_(max)defined in the algorithm is precisely

x_(u_(a_(x, max ))).Third, it can be seen that the travelled distance is monotonicallyincreasing with a, and is unbounded. Hence, for any desired finalposition

${x > {\overset{\sim}{x}}_{u_{{\overset{\sim}{v}}_{{x{\lbrack 0\rbrack}}/t}}}},$there exists a value of a for which x={tilde over (x)}_(u) _(a) . Inparticular, for x=x[t]−W, such a value exists, and we denote it bya_(cut).

Observe that since x_(max), defined in the algorithm, is <x[t]−W, wehave that a_(cut)>a_(x,max). This in not sufficient in order to show novalid maneuver can lead to position ≥x[t]−W; this is implied only formembers of the family U. We now prove that even outside of U, allvelocity profiles which attain a final position of x[t]−W must use anacceleration value of at least a_(cut) on the way, making them invalid,and hence completing the proof.

Assume some velocity profile u satisfies the boundary constraintsu(0)={tilde over (v)}_(x)[0], u(t)={tilde over (v)}_(x)[t]. Moreover,assume it attains some final position {tilde over (x)}_(u)>x[t]−W. Wethus obtain:∫₀ ^(t) u(τ)dτ≥∫ ₀ ^(t) u _(a) _(cut) (τ)dτ.Assume u≥u_(a) _(cut) for all τ. In particular,u(t_(top)(a_(cut)))≥u_(a) _(cut) (t_(top)(a_(cut))). From the mean valuetheorem, there exists ζ0 [0, t_(top)(a_(cut))] s.t.

${{u^{\prime}(\zeta)} = {\frac{{u( {t_{top}( a_{cut} )} )} - {u(0)}}{t_{top}( a_{cut} )} = {{\frac{{u( {t_{top}( a_{cut} )} )} - {u_{a_{cut}}(0)}}{t_{top}( a_{cut} )} \geq \frac{{u_{a_{cut}}( {t_{top}( a_{cut} )} )} - {u_{a_{cut}}(0)}}{t_{top}( a_{cut} )}} = {a_{cut} > a_{x,\max}}}}},$implying infeasibility of u, as it uses acceleration (that is, u′, thederivative of the velocity) which exceeds a_(x,max).

Now, assume u≥u_(a) _(cut) does not hold for all τ. Then, due to thefact ∫₀ ^(t)u(τ)dτ≥∫₀ ^(t)u_(a) _(cut) (τ)dτ, there must be a pointwhere u>u_(a) _(cut) . If such point τ_(large) exists in[0,t_(op)(a_(cut))], then we can easily use the mean value theorem inthe same manner as above, to obtain ζ0 [0,τ_(large)] where too large anacceleration is used. If such point only exists in [t_(top)(a_(cut)),t],similar argument will give us a point ζ0 [τ_(large),t] in which anacceleration value lesser than −a_(x,max) was used, concluding theproof. Equipped with the above lemmas, Theorem 2's proof is immediate.

Safety Verification—Occlusions

In similar fashion to dealing with observed objects, we can define theextension for cautiousness w.r.t. occluded objects, with a similartheorem to Theorem 1, proving that cautiousness implies there are neveraccidents of our blame.

Definition 15 (Cautiousness w.r.t. Occluded Objects) A command given attime t is Cautious w.r.t. Occluded Objects if in the case that theexposure time of the object is t+1, and we command a Default EmergencyPolicy (DEP) at t+1, there will not be an accident of our blame.

Lemma 7 If we only give cautious, w.r.t. occluded objects and nonoccluded objects, commands, there will never be an accident of ourblame.

Proof Assume that an accident of our blame occurred at time t, with theexposure time being t′≤t. By cautiousness assumption, the command givenat t′−1 allowed us to command a DEP at t′ without being blamed for anaccident. As there was an accident of our blame, we apparently did notcommand a DEP at time t′. But from t′ on, we were safe w.r.t. nonoccluded objects, hence the command we gave was safe, and there was noaccident of our blame.

Here too, we provide efficient ways to checking cautiousness withrespect to a worst-case assumption over occluded objects, allowing forfeasible, scalable, RSS.

Driving Policy

A driving policy is a mapping from a sensing state (a description of theworld around us) into a driving command (e.g., the command is lateraland longitudinal accelerations for the coming second, which determineswhere and at what speed should the car be in one second from now). Thedriving command is passed to a controller, which aims at actually movingthe car to the desired position/speed.

In the previous sections a formal safety model and proposed constraintson the commands issued by the driving policy that guarantee safety weredescribed. The constraints on safety are designed for extreme cases.Typically, we do not want to even need these constraints, and would liketo construct a driving policy that leads to a comfortable ride. Thefocus of this section is on how to build an efficient driving policy, inparticular, one that requires computational resources that can scale tomillions of cars. For now, this discussion does not address the issue ofhow to obtain the sensing state and assume an utopic sensing state, thatfaithfully represents the world around us without any limitations. Latersections discuss the effect of inaccuracies in the sensing state on thedriving policy.

The problem of defining a driving policy is cast in the language ofReinforcement Learning (RL), as discussed in the sections above. At eachiteration of RL, an agent observes a state describing the world, denoteds_(t), and should pick an action, denoted a_(t), based on a policyfunction, π, that maps states into actions. As a result of its actionand other factors out of its control (such as the actions of otheragents), the state of the world is changed to s_(t)+1. We denote a(state, action) sequence by s=((s₁,a₁), (s₂,a₂), . . . ,(s_(len(s)),a_(len(s))). Every policy induces a probability functionover (state, action) sequences. This probability function may beaffected by the actions taken by the agent, but also depends on theenvironment (and in particular, on how other agents behave). We denoteby P_(π) the probability over (state, action) sequences induced by π.The quality of a policy is defined to be

_(s˜P) _(π) [ρ(s)], where ρ(s) is a reward function that measures howgood the sequence s is. In most case, ρ(s) takes the form ρ(s)=Σ_(t=1)^(len(s))ρ(s_(t), a_(t)), where ρ(s, a) is an instantaneous rewardfunction that measures the immediate quality of being at state s andperforming action a. For simplicity, we stick to this simpler case.

To cast the driving policy problem in the above RL language, let s_(t)be some representation of the road, and the positions, velocities, andaccelerations, of the ego vehicle as well as other road users. Let a_(t)be a lateral and longitudinal acceleration command. The next state,s_(t+1), depends on a_(t) as well as on how the other agents willbehave. The instantaneous reward, ρ(s_(t), a_(t)), may depend on therelative position/velocities/acceleration to other cars, the differencebetween our speed and the desired speed, whether we follow the desiredroute, whether our acceleration is comfortable etc.

One challenge in deciding what action should the policy take at time tstems from the fact that one needs to estimate the long term effect ofthis action on the reward. For example, in the context of drivingpolicy, an action that is taken at time t may seem a good action for thepresent (that is, the reward value ρ(s_(t), a_(t)) is good), but mightlead to an accident after 5 seconds (that is, the reward value in 5seconds would be catastrophic). We therefore need to estimate the longterm quality of performing an action a when the agent is at state s.This is often called the Q-function, namely, Q(s, a) should reflect thelong term quality of performing action a at time s. Given such aQ-function, the natural choice of an action is to pick the one withhighest quality, π(s)=argmax_(a) Q(s, a).

The immediate questions are how to define Q and how to evaluate Qefficiently. Let us first make the (completely non-realistic)simplifying assumption that s_(t)+1 is some deterministic function of(s_(t), a_(t)), namely, s_(t)+1=ƒ(s_(t), a_(t)). One familiar withMarkov Decision Processes (MDPs), will notice that this assumption iseven stronger than the Markovian assumption of MDPs (i.e., that s_(t)+1is conditionally independent of the past given (s_(t), a_(t))). As notedin [5], even the Markovian assumption is not adequate for multi-agentscenarios, such as driving, and we will therefore later relax theassumption.

Under this simplifying assumption, given st, for every sequence ofdecisions for T steps, (a₁, . . . , a_(t)+_(T)), we can calculateexactly the future states (s_(t)+1, . . . , s_(t)+_(T)+1) as well as thereward values for times t, . . . , T. Summarizing all these rewardvalues into a single number, e.g. by taking their sum Σ_(τ=t)^(T)ρ(s_(τ), a_(τ)), we can define Q(s, a) as follows:

${{Q( {s,a} )} = {\max\limits_{({a_{t},\ldots\;,{a_{t} + T}}}\;{\sum_{\tau = t}^{T}{\rho( {s_{\tau},a_{\tau}} )}}}}\mspace{14mu}$s.t.  s_(t) = s, a_(t) = a, ∀τ, s_(τ + 1) = f(s_(τ), a_(τ))

That is, Q(s, a) is the best future we can hope for, if we are currentlyat state s and immediately perform action a.

Let us discuss how Q may be calculated. The first idea is to discretizethe set of possible actions, A, into a finite set Â, and simply traverseall action sequences in the discretized set. Then, the runtime isdominated by the number of discrete action sequences, |Â|^(T). If Ârepresents 10 lateral accelerations and 10 longitudinal accelerations,we obtain 100^(T) possibilities, which becomes infeasible even for smallvalues of T. While there are heuristics for speeding up the search (e.g.coarse-to-fine search), this brute-force approach requires tremendouscomputational power.

The parameter T is often called the “time horizon of planning”, and itcontrols a natural tradeoff between computation time and quality ofevaluation—the larger T is, the better our evaluation of the currentaction (since we explicitly examine its effect deeper into the future),but on the other hand, a larger T increases the computation timeexponentially. To understand why we may need a large value of T,consider a scenario in which we are 200 meters before a highway exit andwe should take it. When the time horizon is long enough, the cumulativereward will indicate if at some time τ between t and t+T we have arrivedto the exit lane. On the other hand, for a short time horizon, even ifwe perform the right immediate action we will not know if it will leadus eventually to the exit lane.

A different approach attempts to perform offline calculations in orderto construct an approximation of Q, denoted {circumflex over (Q)}, andthen during the online run of the policy, use {circumflex over (Q)} asan approximation to Q, without explicitly rolling out the future. Oneway to construct such an approximation is to discretize both the actiondomain and the state domain. Denote by Â, Ŝ these discretized sets. Anoffline calculation may evaluate the value of Q(s, a) for every (s, a) 0Ŝ H Â. Then, for every a 0 Â we define {circumflex over (Q)}(s_(t), a)to be Q(s, a) for s=argmin_(s) _(0,Ŝ) ∥s−s_(t)∥. Furthermore, based onthe pioneering work of Bellman [2, 3], we can calculate Q(s, a) forevery (s, a) 0 Ŝ H Â, based on dynamic programming procedures (such asthe Value Iteration algorithm), and under our assumptions, the totalruntime is order of T|Â| |Ŝ|. The main problem with this approach isthat in any reasonable approximation, Ŝ is extremely large (due to thecurse of dimensionality). Indeed, the sensing state should represent 6parameters for every other relevant vehicle in the sense—thelongitudinal and lateral position, velocity, and acceleration. Even ifwe discretize each dimension to only 10 values (a very crudediscretization), since we have 6 dimensions, to describe a single car weneed 10⁶ states, and to describe k cars we need 10^(6k) states. Thisleads to unrealistic memory requirements for storing the values of Q forevery (s, a) in Ŝ H Â.

One approach for dealing with this curse of dimensionality is torestrict Q to come from a restricted class of functions (often called ahypothesis class), such as linear functions over manually determinedfeatures or deep neural networks. For example, consider a deep neuralnetwork that approximates Q in the context of playing Atari games. Thisleads to a resource-efficient solution, provided that the class offunctions that approximate Q can be evaluated efficiently. However,there are several disadvantages of this approach. First, it is not knownif the chosen class of functions contains a good approximation to thedesired Q function. Second, even if such function exists, it is notknown if existing algorithms will manage to learn it efficiently. Sofar, there are not many success stories for learning a Q function forcomplicated multi-agent problems, such as the ones we are facing indriving. There are several theoretical reasons why this task isdifficult. As mentioned regarding the Markovian assumption, underlyingexisting methods are problematic. But, a more severe problem is a verysmall signal-to-noise ratio due to the time resolution of decisionmaking, as explained below.

Consider a simple scenario in which a vehicle needs to change lane inorder to take a highway exit in 200 meters and the road is currentlyempty. The best decision is to start making the lane change. Decisionsmay be made every 0.1 second, so at the current time t, the best valueof Q(s_(t), a) should be for the action a corresponding to a smalllateral acceleration to the right. Consider the action a′ thatcorresponds to zero lateral acceleration. Since there is a very littledifference between starting the change lane now, or in 0.1 seconds, thevalues of Q(s_(t), a) and Q(s_(t), a′) are almost the same. In otherwords, there is very little advantage for picking a over a′. On theother hand, since we are using a function approximation for Q, and sincethere is noise in measuring the state s_(t), it is likely that ourapproximation to the Q value is noisy. This yields a very smallsignal-to-noise ratio, which leads to an extremely slow learning,especially for stochastic learning algorithms which are heavily used forthe neural networks approximation class. However, as noted in, thisproblem is not a property of any particular function approximationclass, but rather, it is inherent in the definition of the Q function.

In summary, available approaches can be roughly divided into two camps.The first one is the brute-force approach which includes searching overmany sequences of actions or discretizing the sensing state domain andmaintaining a huge table in memory. This approach can lead to a veryaccurate approximation of Q but requires unlimited resources, either interms of computation time or in terms of memory. The second one is aresource efficient approach in which we either search for shortsequences of actions or we apply a function approximation to Q. In bothcases, we pay by having a less accurate approximation of Q that mightlead to poor decisions.

The approach described herein includes constructing a Q function that isboth resource-efficient and accurate is to depart from geometricalactions and to adapt a semantic action space, as described in the nextsubsection.

Semantic Approach

As a basis for the disclosed semantic approach, consider a teenager thatjust got his driving license. His father sits next to him and gives him“driving policy” instructions. These instructions are not geometric—theydo not take the form “drive 13.7 meters at the current speed and thenaccelerate at a rate of 0.8 m/s²”. Instead, the instructions are ofsemantic nature—“follow the car in front of you” or “quickly overtakethat car on your left.” We formalize a semantic language for suchinstructions, and use them as a semantic action space. We then definethe Q function over the semantic action space. We show that a semanticaction can have a very long time horizon, which allows us to estimateQ(s, a) without planning for many future semantic actions. Yes, thetotal number of semantic actions is still small. This allows us toobtain an accurate estimation of the Q function while still beingresource efficient. Furthermore, as we show later, we combine learningtechniques for further improving the quality function, while notsuffering from a small signal-to-noise ratio due to a significantdifference between different semantic actions.

Now define a semantic action space. The main idea is to define lateraland longitudinal goals, as well as the aggressiveness level of achievingthem. Lateral goals are desired positions in lane coordinate system(e.g., “my goal is to be in the center of lane number 2”). Longitudinalgoals are of three types. The first is relative position and speed withrespect to other vehicles (e.g., “my goal is to be behind car number 3,at its same speed, and at a distance of 2 seconds from it”). The secondis a speed target (e.g., “drive at the allowed speed for this road times110%”). The third is a speed constraint at a certain position (e.g.,when approaching a junction, “speed of 0 at the stop line”, or whenpassing a sharp curve, “speed of at most 60 kmh at a certain position onthe curve”). For the third option, we can instead apply a “speedprofile” (few discrete points on the route and the desired speed at eachof them). A reasonable number of lateral goals is bounded by 16=4×4 (4positions in at most 4 relevant lanes). A reasonable number oflongitudinal goals of the first type is bounded by 8×2×3=48 (8 relevantcars, whether to be in front or behind them, and 3 relevant distances).A reasonable number of absolute speed targets are 10, and a reasonableupper bound on the number of speed constraints is 2. To implement agiven lateral or longitudinal goal, we need to apply acceleration andthen deceleration (or the other way around). The aggressiveness ofachieving the goal is a maximal (in absolute value)acceleration/deceleration to achieve the goal. With the goal andaggressiveness defined, we have a closed form formula to implement thegoal, using kinematic calculations. The only remaining part is todetermine the combination between the lateral and longitudinal goals(e.g., “start with the lateral goal, and exactly at the middle of it,start to apply also the longitudinal goal”). A set of 5 mixing times and3 aggressiveness levels seems more than enough. All in all, we haveobtained a semantic action space whose size is ≈10⁴.

It is worth mentioning that the variable time required for fulfillingthese semantic actions is not the same as the frequency of the decisionmaking process. To be reactive to the dynamic world, we should makedecisions at a high frequency—in our implementation, every 100 ms. Incontrast, each such decision is based on constructing a trajectory thatfulfills some semantic action, which will have a much longer timehorizon (say, 10 seconds). We use the longer time horizon since it helpsus to better evaluate the short term prefix of the trajectory. The nextsubsection discusses the evaluation of semantic actions, but beforethat, we argue that semantic actions induce a sufficient search space.

As discussed above, a semantic action space induces a subset of allpossible geometrical curves, whose size is exponentially smaller (in T)than enumerating all possible geometrical curves. The first immediatequestion is whether the set of short term prefixes of this smallersearch space contains all geometric commands that we will ever want touse. This is indeed sufficient in the following sense. If the road isfree of other agents, then there is no reason to make changes exceptsetting a lateral goal and/or absolute acceleration commands and/orspeed constraints on certain positions. If the road contains otheragents, we may want to negotiate the right of way with the other agents.In this case, it suffices to set longitudinal goals relatively to theother agents. The exact implementation of these goals in the long runmay vary, but the short term prefixes will not change by much. Hence, weobtain a very good cover of the relevant short term geometricalcommands.

Constructing an Evaluation Function for Semantic Actions

We have defined a semantic set of actions, denoted by A^(s). Given thatwe are currently in state, s, we need a way to choose the best a^(s) 0A^(s). To tackle this problem, we follow a similar approach to theoptions mechanism of [6]. The basic idea is to think of a^(s) as ameta-action (or an option). For each choice of a meta-action, weconstruct a geometrical trajectory (s₁, a₁), . . . , (s_(T), a_(T)) thatrepresents an implementation of the meta-action, a^(s). To do so we ofcourse need to know how other agents will react to our actions, but fornow we are still relying on (the non-realistic) assumption thats_(t+1)=ƒ(s_(t), a_(t)) for some known deterministic function ƒ. We cannow use

$\frac{1}{T}{\sum_{t = 1}^{T}{\rho( {s_{t},a_{t}} )}}$as a good approximation of the quality of performing the semantic actiona^(s) when we are at state s¹.

This approach can yield a powerful driving policy. However, in somesituations a more sophisticated quality function may be needed. Forexample, suppose that we are following a slow truck before an exit lane,where we need to take the exit lane. One semantic option is to keepdriving slowly behind the truck. Another one is to overtake the truck,hoping that later we can get back to the exit lane and make the exit ontime. The quality measure described previously does not consider whatwill happen after we will overtake the truck, and hence we will notchoose the second semantic action even if there is enough time to makethe overtake and return to the exit lane. Machine learning can help usto construct a better evaluation of semantic actions that will take intoaccount more than the immediate semantic actions. As previouslydiscussed, learning a Q function over immediate geometric actions isproblematic due to the low signal-to-noise ratio (the lack ofadvantage). This is not problematic when considering semantic actions,both because there is a large difference between performing thedifferent semantic actions and because the semantic time horizon (howmany semantic actions we take into account) is very small (probably lessthan three in most cases).

Another potential advantage of applying machine learning is for the sakeof generalization: we may set an adequate evaluation function for everyroad, by a manual inspection of the properties of the road, which mayinvolve some trial and error. But, can we automatically generalize toany road? Here, a machine learning approach, as discussed above, can betrained on a large variety of road types so as to generalize to unseenroads as well. The semantic action space according to the disclosedembodiments may allow for potential benefits: semantic actions containinformation on a long time horizon, hence we can obtain a very accurateevaluation of their quality while being resource efficient.

The Dynamics of the Other Agents

So far, we have relied on the assumption that s_(t+1) is a deterministicfunction of s_(t) and a_(t). As emphasized previously, this assumptionis not completely realistic as our actions affect the behavior of otherroad users. While we do take into account some reactions of other agentsto our actions (for example, we assume that if we will perform a safecut-in than the car behind us will adjust its speed so as not to hit usfrom behind), it is not realistic to assume that we model all of thedynamics of other agents. The solution to this problem is to re-applythe decision making at a high frequency, and by doing this, constantlyadapt our policy to the parts of the environment that are beyond ourmodeling. In a sense, one can think of this as a Markovization of theworld at every step.

Sensing

This section describes the sensing state, which is a description of therelevant information of the scene, and forms the input to the drivingpolicy module. By and large, the sensing state contains static anddynamic objects. The static objects are lanes, physical road delimiters,constraints on speed, constraints on the right of way, and informationon occluders (e.g., a fence that occludes relevant part of a mergingroad). Dynamic objects are vehicles (e.g., bounding box, speed,acceleration), pedestrians (bounding box, speed, acceleration), trafficlights, dynamic road delimiters (e.g., cones at a construction area),temporary traffic signs and police activity, and other obstacles on theroad (e.g., an animal, a mattress that fell from a truck, etc.).

In any reasonable sensor setting, we cannot expect to obtain the exactsensing state, s. Instead, we view raw sensor and mapping data, which wedenote by x 0 X, and there is a sensing system that takes x and producesan approximate sensing state.

Definition 16 (Sensing system) Let S denotes the domain of sensing stateand let X be the domain of raw sensor and mapping data. A sensing systemis a function ŝ: X→S.

It is important to understand when we should accept ŝ(x) as a reasonableapproximation to s. The ultimate way to answer this question is byexamining the implications of this approximation on the performance ofour driving policy in general, and on the safety in particular.Following our safety-comfort distinction, here again we distinguishbetween sensing mistakes that lead to non-safe behavior and sensingmistakes that affect the comfort aspects of the ride. Before addressingthe details, the type of errors a sensing system might make include:

-   -   False negative: the sensing system misses an object    -   False positive: the sensing system indicates a “ghost” object    -   Inaccurate measurements: the sensing system correctly detects an        object but incorrectly estimates its position or speed    -   Inaccurate semantic: the sensing system correctly detects an        object but misinterpret its semantic meaning, for example, the        color of a traffic light

Comfort

Recall that for a semantic action a, we have used Q(s, a) to denote ourevaluation of a given that the current sensing state is s. Our policypicks the action π(s)=argmax_(a) Q(s, a). If we inject ŝ(x) instead of sthen the selected semantic action would be π(ŝ(x))=argmax_(a) Q(s(x),a). If π(ŝ(x))=π(s) then ŝ(x) should be accepted as a good approximationto s. But, it is also not bad at all to pick π(ŝ(x)) as long as thequality of π(ŝ(x)) w.r.t. the true state, s, is almost optimal, namely,Q(s, π(ŝ(x)))≥Q(s, π(s))−ϵ, for some parameter ϵ. We say that ŝ isϵ-accurate w.r.t. Q in such case. Naturally, we cannot expect thesensing system to be ϵ-accurate all the time. We therefore also allowthe sensing system to fail with some small probability δ. In such a casewe say that s is Probably (w.p. of at least 1-δ), Approximately (up toϵ), Correct, or PAC for short (borrowing Valiant's PAC learningterminology).

We may use several (ϵ, δ) pairs for evaluating different aspects of thesystem. For example, we can choose three thresholds, ϵ₁<ϵ₂<ϵ₃ torepresent mild, medium, and gross mistakes, and for each one of them seta different value of δ. This leads to the following definition.

Definition 17 (PAC sensing system) Let ((ϵ₁, δ₁), . . . , (ϵ_(k),δ_(k)))be a set of (accuracy,confidence) pairs, let S be the sensing statedomain, let X be the raw sensor and mapping data domain, and let D be adistribution over X×S. Let A be an action space, Q: S×A→|be a qualityfunction, and π: S→A be such that π(s)∈argmax_(a) Q(s, a). A sensingsystem, ŝ: X→S, is Probably-Approximately-Correct (PAC) with respect tothe above parameters if for every i∈{1, . . . , k} we have thatP_((x,s)˜D)[Q(s, π(ŝ(x)))≥Q(s, π(s))−ϵ_(i)]≥1−δ_(i).

Here, the definition depends on a distribution D over X×S. It isimportant to emphasize that we construct this distribution by recordingdata of many human drivers but not by following the particular policy ofour autonomous vehicle. While the latter seems more adequate, itnecessitates online validation, which makes the development of thesensing system impractical. Since the effect of any reasonable policy onD is minor, by applying simple data augmentation techniques we canconstruct an adequate distribution and then perform offline validationafter every major update of the sensing system. The definition providesa sufficient, but not necessary, condition for comfort ride using ŝ. Itis not necessary because it ignores the important fact that short termwrong decisions have little effect on the comfort of the ride. Forexample, suppose that there is a vehicle 100 meters ahead, and it isslower than the host vehicle. The best decision would be to startaccelerating slightly now. If the sensing system misses this vehicle,but will detect it in the next time (after 100 milli-seconds), then thedifference between the two rides will not be noticeable. To simplify thepresentation, we have neglected this issue and required a strongercondition. The adaptation to a multi-frame PAC definition isconceptually straightforward, but is more technical.

We next derive design principles that follow from the above PACdefinition. Recall that we have described several types of sensingmistakes. For mistakes of types false negative, false positive, andinaccurate semantic, either the mistakes will be on non-relevant objects(e.g., a traffic light for left turn when we are proceeding straight),or they will be captured by the δ part of the definition. We thereforefocus on the “inaccurate measurements” type of errors, which happensfrequently.

Somewhat surprisingly, we will show that the popular approach ofmeasuring the accuracy of a sensing system via ego-accuracy (that is, bymeasuring the accuracy of position of every object with respect to thehost vehicle) is not sufficient for ensuring PAC sensing system. We willthen propose a different approach that ensures PAC sensing system, andwill show how to obtain it efficiently. We start with some additionaldefinitions.

For every object o in the scene, let p(o), {circumflex over (p)}(o) bethe positions of o in the coordinate system of the host vehicleaccording to s, ŝ(x), respectively. Note that the distance between o andthe host vehicle is ∥p∥. The additive error of {circumflex over (p)} is∥p(o)−{circumflex over (p)}(o)∥. The relative error of {circumflex over(p)}(o), w.r.t. the distance between o and the host vehicle, is theadditive error divided by ∥p(o)∥, namely

$\frac{{{\hat{p}(o)} - {p(o)}}}{{p(o)}},$

It is not realistic to require that the additive error is small for faraway objects. Indeed, consider o to be a vehicle at a distance of 150meters from the host vehicle, and let ϵ be of moderate size, say ϵ=0.1.For additive accuracy, it means that we should know the position of thevehicle up to 10 cm of accuracy. This is not realistic for reasonablypriced sensors. On the other hand, for relative accuracy we need toestimate the position up to 10%, which amounts to 15 m of accuracy. Thisis feasible to achieve (as described below).

A sensing system, ŝ, positions a set of objects, O, in an ϵ-ego-accurateway, if for every o∈O, the (relative) error between p(o) and {circumflexover (p)}(o) is at most ϵ. The following example demonstrates that anϵ-ego-accurate sensing state does not guarantee PAC sensing system withrespect to every reasonable Q. Indeed, consider a scenario in which thehost vehicle drives at a speed of 30 m/s, and there is a stopped vehicle150 meters in front of it. If this vehicle is in the ego lane, and thereis no option to change lanes in time, we must start decelerating now ata rate of at least 3 m/s² (otherwise, we will either not stop in time orwe will need to decelerate strongly later). On the other hand, if thevehicle is on the side of the road, we don't need to apply a strongdeceleration. Suppose that p(o) is one of these cases while {circumflexover (p)}(o) is the other case, and there is a 5 meters differencebetween these two positions. Then, the relative error of {circumflexover (p)}(o) is

$\frac{{{\overset{\hat{}}{p}(0)} - {p(0)}}}{{p(0)}} = {\frac{5}{150} = {\frac{1}{30} \leq {{0.0}3{4.}}}}$

That is, the sensing system may be ϵ-ego-accurate for a rather smallvalue of ϵ (less than 3.5% error), and yet, for any reasonable Qfunction, the values of Q are completely different since we areconfusing between a situation in which we need to brake strongly and asituation in which we do not need to brake strongly.

The above example shows that ϵ-ego-accuracy does not guarantee that oursensing system is PAC. Whether there is another property that issufficient for PAC sensing system depends on Q. We will describe afamily of Q functions for which there is a simple property of thepositioning that guarantees PAC sensing system. The problem ofϵ-ego-accuracy is that it might lead to semantic mistakes—in theaforementioned example, even though ŝ was ϵ-ego-accurate with ϵ<3.5%, itmis-assigned the vehicle to the correct lane. To solve this problem, werely on semantic units for lateral position.

Definition 18 (semantic units) A lane center is a simple natural curve,namely, it is a differentiable, injective, mapping

: [a, b]→|³, where for every a≤t₁<t₂≤b we have that the lengthLength(t₁, t₂):=∫_(r=t) ₁ ^(t) ² |

′(τ)|dτ equals to t₂−t₁. The width of the lane is a function w:[a,b]→|₊. The projection of a point x∈|³ onto the curve is the point on thecurve closest to x, namely, the point

(t_(x)) for t_(x)=argmin_(t∈[a,b])∥

(t)−x∥. The semantic longitudinal position of x w.r.t. the lane is t_(x)and the semantic lateral position w.r.t the lane is

(t_(x))/w(t_(x)). Semantic speed and acceleration are defined as firstand second derivatives o/the above.

Similarly to geometrical units, for semantic longitudinal distance weuse relative error: if ŝ induces a semantic longitudinal distance of{circumflex over (p)}(o) for some object, while the true distance isp(o), then the relative error is

$\frac{❘{{\hat{p}(o)} - {p(o)}}❘}{\max\{ {{p(o)},1} \}}$(where the maximum in the denominator deals with cases in which theobject has almost the same longitudinal distance (e.g., a car next to uson another lane). Since semantic lateral distances are small we can useadditive error for them. This leads to the following definition:

Definition 19 (error in semantic units) Let

be a lane and suppose that the semantic longitudinal distance of thehost vehicle w.r.t. the lane is 0. Let x∈

³ be a point and let p_(lat)(x), p_(lon)(x) be the semantic lateral andlongitudinal distances to the point w.r.t. the lane. Let {circumflexover (p)}_(lat)(x), {circumflex over (p)}_(lon)(x) be approximatedmeasurements. The distance between {circumflex over (p)} and p w.r.t. xis defined as

${d( {\hat{p},{p;x}} )} = {\max\{ {{❘{{{\hat{p}}_{lat}(x)} - {p_{lat}(x)}}❘},\frac{❘{{{\hat{p}}_{lon}(x)} - {p_{lon}(x)}}❘}{\max\{ {{p_{lon}(x)},1} \}}} \}}$

The distance of the lateral and longitudinal velocities is definedanalogously. Equipped with the above definition, we are ready to definethe property of Q and the corresponding sufficient condition for PACsensing system.

Definition 20 (Semantically-Lipschitz Q) A Q function isL-semantically-Lipschitz if for every a, s, ŝ, |Q(s, a)−Q(ŝ(x), a)|≤Lmax_(o) d({circumflex over (p)}, p; o), where {circumflex over (p)}, pare the measurements induced by s, ŝ on an object o.

As an immediate corollary we obtain:

Lemma 8 if Q is L-semantically-Lipschitz and a sensing system g producessemantic measurements such that with probability of at least 1−δ we haved({circumflex over (p)}, p; o)≤0/L then ŝ is a PAC sensing system withparameters 0, δ.

Safety

This section discusses the potential for sensing errors that can lead tounwanted behaviors. As mentioned before, the policy is provably safe, inthe sense that it won't lead to accidents of the host AV's blame. Suchaccidents might still occur due to hardware failure (e.g., a breakdownof all the sensors or exploding tire on the highway), software failure(a significant bug in some of the modules), or a sensing mistake. Ourultimate goal is that the probability of such events will be extremelysmall a probability of 10 for such an accident per hour, To appreciatethis number, the average number of hours driver in the U.S. spends onthe road is (as of 2016) less than 300 hours. So, in expectation, onewould need to live 3.3 million years to be in an accident resulting fromone of these types of events.

We first define what is a safety-related sensing error. Recall that atevery step, our policy picks the value of a that maximizes Q(s, a),namely, π(s)=argmax_(a) Q(s, a). We ensure safety by letting Q(s, a)=−∞for every action a that is not cautious (see Definition 14). Therefore,the first type of safety-critic sensing mistake is if our sensing systemleads to picking a non-safe action. Formally, letting π(ŝ(x))=argmax_(a)Q(ŝ(x), a) be the decision according to ŝ, we say that ŝ leads to asafety-critic miss if Q(s, π(ŝ(x)))=−∞. The second type of safety-criticsensing mistake is if all the actions are non-safe according to § (x),and we must apply the standard emergency policy (e.g., braking hard),while according to s there is a safe action, namely, max_(a), Q(s,a)>−∞. This is dangerous when our speed is high and there is a carbehind us. We call such mistake a safety-critic ghost.

Usually, a safety-critic miss is caused by a false negative while asafety-critic ghost is caused by a false positive. Such mistakes canalso be caused from significantly incorrect measurements, but in mostcases, our comfort Objective ensures we are far away from the boundaryof the safety definitions, and therefore reasonable measurements errorsare unlikely to lead to a safety-critic mistake. How can we ensure thatthe probability of safety-critic mistakes will be very small, say,smaller than 10⁻⁹ per hour? As followed from Lemma 1, without makingfurther assumptions we need to check our system on more than 10⁹ hoursof driving. This is unrealistic (or at least extremely challenging)—itamounts to recording the driving of 3.3 million cars over a year.Furthermore, building a system that achieves such a high accuracy is agreat challenge. A solution for both the system design and validationchallenges is to rely on several sub-systems, each of which isengineered independently and depends on a different technology, and thesystems are fused together in a way that ensures boosting of theirindividual accuracy.

Suppose we build three sub-systems, denoted, s₁, s₂, s₃ (the extensionto more than 3 is straightforward). Each sub-system receives a andshould output safe/non-safe. Actions for which the majority of thesub-systems (2 in our case) accept as safe are considered safe. If thereis no action that is considered safe by at least 2 sub-systems, then thedefault emergency policy is applied. The performance of this fusionscheme is analyzed as follows based on the following definition:

Definition 21 (One side c-approximate independent) Two Bernoulli randomvariables r₁, r₂ are called one side c-approximate independent if

[r ₁ ∧r ₂ ]≤c

[r ₁ ]

[r ₂].

For i 0 {1,2,3}, denote by e_(i) ^(m), e_(i) ^(g) the Bernoulli randomvariables that indicate if sub-system i performs a safety-criticmiss/ghost respectively. Similarly, e^(m), e^(g) indicate asafety-critic miss/ghost of the fusion system. We rely on the assumptionthat for any pair i≠j, the random variables e_(i) ^(m), e_(j) ^(m) areone sided c-approximate independent, and the same holds for e_(i) ^(g),e_(j) ^(g). Before explaining why this assumption is reasonable, let usfirst analyze its implication. We can bound the probability of e^(m) by:

${{\mathbb{P}}\lbrack e^{m} \rbrack} = {{{{{\mathbb{P}}\lbrack {e_{1}^{m} \land e_{2}^{m} \land e_{3}^{m}} \rbrack} + {\sum\limits_{j = 1}^{3}{{\mathbb{P}}\lbrack {{\neg e_{j}^{m}} \land \land_{i \neq j}e_{i}^{m}} \rbrack}}} \leq {{3{{\mathbb{P}}\lbrack {e_{1}^{m} \land e_{2}^{m} \land e_{3}^{m}} \rbrack}} + {\underset{j = 1}{\sum\limits^{3}}{{\mathbb{P}}\lbrack {{\neg e_{j^{m}}} \land \land_{i \neq j}e_{i}^{m}} \rbrack}}}} = {{\sum\limits_{j = 1}^{3}{{\mathbb{P}}\lbrack {\land_{i \neq j}e_{i}^{m}} \rbrack}} \leq {c{\sum\limits_{j = 1}^{3}{\prod\limits_{i \neq j}{{{\mathbb{P}}\lbrack e_{i}^{m} \rbrack}.}}}}}}$

Therefore, if all sub-systems have

[e_(i) ^(m)]≤p then

[e^(m)]≤3cp². The exact same derivation holds for the safety-criticghost mistakes. By applying a union bound we therefore conclude:

Corollary 2 Assume that for any pair i≠j the random variables e_(i)^(m), e_(j) ^(m) are one sided c-approximate independent, and the sameholds for e_(i) ^(g), e_(j) ^(g). Assume also that for every i,

[e_(i) ^(m)]≤p and

[e_(i) ^(g)]≤p. Then,

[e ^(m) ∨e ^(g)]≤6cp ².

This corollary allows us to use significantly smaller data sets in orderto validate the sensing system. For example, if we would like to achievea safety-critic mistake probability of 10⁻⁹, instead of taking order of10⁹ examples, it suffices to take order of 10⁵ examples and test eachsystem separately.

There may be pairs of sensors that yield non-correlated errors. Forexample, radar works well in bad weather conditions but might fail dueto non-relevant metallic objects, as opposed to camera that is affectedby bad weather but is not likely to be affected by metallic objects.Seemingly, camera and lidar have common sources of error—e.g., both areaffected by foggy weather, heavy rain, or snow. However, the type oferrors for camera and lidar would be different—a camera might missobjects due to bad weather and lidar might detect a ghost due toreflections from particles in the air. Since we have distinguishedbetween the two types of errors, the approximate independency is stilllikely to hold.

Our definition of safety-important ghost requires that all actions arenon-safe by at least two sensors, Even in difficult conditions (e.g.,heavy fog), this is unlikely to happen. The reason is that in suchsituations, systems that are affected by the difficult conditions (e.g.,the lidar), will dictate a very defensive driving, as they can declarehigh velocity and lateral maneuver to be non-safe actions. As a result,the host AV will drive slowly, and then even if an emergency stop isrequired, it is not dangerous due to the low speed of driving.Therefore, our definition yields an adaptation of the driving style tothe conditions of the road.

Building a Scalable Sensing System

The requirements from a sensing system, both in terms of comfort andsafety, have been described. Next, an approach for building a sensingsystem that meets these requirements while being scalable is described.There are three main components of the sensing system. The first is longrange, 360 degrees coverage, of the scene based on cameras. The threemain advantages of cameras are: (1) high resolution, (2) texture, (3)price. The low price enables a scalable system. The texture enables tounderstand the semantics of the scene, including lane marks, trafficlight, intentions of pedestrians, and more. The high resolution enablesa long range of detection. Furthermore, detecting lane marks and objectsin the same domain enables excellent semantic lateral accuracy. The twomain disadvantages of cameras are: (1) the information is 2D andestimating longitudinal distance is difficult, (2) sensitivity tolighting conditions (low sun, bad weather). We overcome thesedifficulties using the next two components of our system.

The second component of our system is a semantic high-definition mappingtechnology, called Road Experience Management (REM) (which involvesnavigation based on target trajectories predetermined and stored forroad segments along with an ability to determine precise locations alongthe target trajectories based on the location (e.g., in images) ofrecognized landmarks identified in the environment of the host vehicle).A common geometrical approach to map creation is to record a cloud of 3Dpoints (obtained by a lidar) in the map creation process, and then,localization on the map is obtained by matching the existing lidarpoints to the ones in the map. There are several disadvantages of thisapproach. First, it requires a large memory per kilometer of mappingdata, as we need to save many points. This necessitates an expensivecommunication infrastructure. Second, not all cars may be equipped withlidar sensors, and therefore, the map is updated very infrequently. Thisis problematic as changes in the road can occur (construction zones,hazards), and the “time-to-reflect-reality” of lidar-based mappingsolutions is large. In contrast, REM follows a semantic-based approach.The idea is to leverage the large number of vehicles that are equippedwith cameras and with software that detects semantically meaningfulobjects in the scene (lane marks, curbs, poles, traffic lights, etc.).Nowadays, many new cars are equipped with ADAS systems which can beleveraged for crowd-sourced map creation. Since the processing is doneon the vehicle side, only a small amount of semantic data should becommunicated to the cloud. This allows a very frequent update of the mapin a scalable way. In addition, the autonomous vehicles can receive thesmall sized mapping data over existing communication platforms (thecellular network). Finally, highly accurate localization on the map canbe obtained based on cameras, without the need for expensive lidars.

REM may be used for several purposes. First, it gives us a foresight onthe static structure of the road (we can plan for a highway exit way inadvance). Second, it gives us another source of accurate information ofall of the static information, which together with the camera detectionsyields a robust view of the static part of the world. Third, it solvesthe problem of lifting the 2D information from the image plane into the3D world as follows. The map describes all of the lanes as curves in the3D world. Localization of the ego vehicle on the map enables totrivially lift every object on the road from the image plane to its 3Dposition. This yields a positioning system that adheres to the accuracyin semantic units. A third component of the system may be complementaryradar and lidar systems. These systems may serve two purposes. First,they can offer extremely high levels of accuracy for augmenting safety.Second, they can give direct measurements on speed and distances, whichfurther improves the comfort of the ride.

The following sections include technical lemmas and several practicalconsiderations of the RSS system.

Lemma 9 For all x 0 [0,0.1], it holds that 1−x>e^(−2x). Proof Letƒ(x)=1−x−e^(−2x). Our goal is to show it is ≥0 for x 0 [0,0.1]. Notethat ƒ′(0)=0, and it is therefore sufficient to have that ƒ(x)≥0 in theaforementioned range. Explicitly, ƒ′(x)=−1+2e^(−2x). Clearly, ƒ′(0)=1,and it is monotonically decreasing, hence it is sufficient to verifythat ƒ′(0.1)>0, which is easy to do numerically, ƒ′(0.1)≈0.637.

Efficient Cautiousness Verification—Occluded Objects

As with non-occluded objects, we can check whether giving the currentcommand, and after it, the DEP, is RSS, For this, we unroll our futureuntil t_(brake), when assuming the exposure time is 1 and we thencommand DEP, which suffices for cautiousness by definition. For all t′0[0,t_(brake)], we check whether a blameful accident can occur—whenassuming worst case over the occluded object. We use some of our worstcase maneuvers and safe distance rules. We take an occluder basedapproach to find interest points—namely, for each occluding object, wecalculate the worst case. This is a crucial efficiency-driven approach—apedestrian, for example, can be hidden in many positions behind a car,and can perform many maneuvers, but there's a single worst case positionand maneuver it can perform.

Next, consider the more elaborate case, that of the occluded pedestrian.Consider an occluded area behind a parked car. The closest points in anoccluded area and the front/side of our car c may be found, for example,by their geometrical properties (triangles, rectangles). Formally, wecan consider the occluded area as a union of a small number of convexregions of simple shape, and treat each of them separately. Furthermore,it can be seen that a pedestrian can run into the front of the car(under the v_(limit) constraint) from the occluded area IFF he can do itusing the shortest path possible. Using the fact that the maximaldistance which can be travelled by the pedestrian is v_(limit)·t′, weobtain a simple check for a frontal hit possibility. As for a side hit,we note that in case the path is shorter than v_(limit)·t′, we areresponsible IFF our lateral velocity is greater than μ, in the directionof the hit. Disclosed is an algorithm for cautiousness verification withrespect to occluded pedestrians, which is described here in free pseudocode. The crucial part, that of checking existence of possibility ofblameful accident with a pedestrian occluded by a vehicle, is done inthe simple manner described above.

Algorithm 2: Check cautiousness w.r.t. an occluded pedestrian for t′ ∈[0, t_(brake)] Roll self future until t′ if Exists possibility ofblameful accident with a pedestrian occluded by a vehicle return“non-cautious” return “cautious”

On the Problem of Validating a Simulator

As previously discussed, multi-agent safety may be difficult to validatestatistically as it should be done in an “online” manner. One may arguethat by building a simulator of the driving environment, we can validatethe driving policy in the “lab.” However, validating that the simulatorfaithfully represents reality is as hard as validating the policyitself. To see why this is true, suppose that the simulator has beenvalidated in the sense that applying a driving policy a in the simulatorleads to a probability of an accident of {circumflex over (p)}, and theprobability of an accident of r in the real world is p, with|p−{circumflex over (p)}|<0. (We need that 0 will be smaller than 10⁻⁹.)Next replace the driving policy to be π′. Suppose that with probabilityof 10⁻⁸, π′ performs a weird action that confuses human drivers andleads to an accident. It is possible (and even rather likely) that thisweird action is not modeled in the simulator, without contradicting itssuperb capabilities in estimating the performance of the original policyπ. This proves that even if a simulator has been shown to reflectreality for a driving policy π it is not guaranteed to reflect realityfor another driving policy.

The Lane-Based Coordinate System

One simplifying assumption that can be made in the RSS definition isthat the road is comprised by adjacent, straight lanes, of constantwidth. The distinction between lateral and longitudinal axes, along withan ordering of longitudinal position, may play a significant role inRSS. Moreover, the definition of those directions is clearly based onthe lane shape. A transformation from (global) positions on the plane,to a lane-based coordinate system reduces the problem to the original,“straight lane of constant width,” case.

Assume that the lane's center is a smooth directed curve r on the plane,where all of its pieces, denoted r⁽¹⁾, . . . . , r^((k)), are eitherlinear, or an arc. Note that smoothness of the curve implies that nopair of consecutive pieces can be linear. Formally, the curve maps a“longitudinal” parameter, Y0 [Y_(min), Y_(max)]⊂|, into the plane,namely, the curve is a function of the form r:[Y_(min), Y_(max)]→|². Wedefine a continuous lane-width function w:[Y_(min), Y_(max)]→|₊, mappingthe longitudinal position Y into a positive lane width value. For eachY, from smoothness of r, we can define the normal unit-vector to thecurve at position Y, denoted r^(⊥)(Y). We naturally define the subset ofpoints on the plane which reside in the lane as follows:R={r(Y)+aw( )r ^(⊥)(Y)|Y0[Y _(min) ,Y _(max)],α0[±½]}

Informally, our goal is to construct a transformation ϕ of R into suchthat for two cars which are on the lane, their “logical ordering” willbe preserved: if c_(r), is “behind” c_(f) on the curve, thenϕ(c_(r))_(y)<ϕ(c_(f))_(y). If c_(l) is “to the left of” c_(r) on thecurve, then ϕ(c_(l))_(x)<ϕ(c_(r))_(x). Where, as in RSS, we willassociate the y-axis with the “longitudinal” axis, and the x-axis withthe “lateral”.

To define ϕ, we rely on the assumption that for all i, if r^((i)) is anarc of radius ρ, then the width of the lane throughout r^((i)) is ≤ρ/2.Note that this assumption holds for any practical road. The assumptiontrivially implies that for all (x′,y′) 0 R, there exists a unique pairY′0 [Y_(min), Y_(max)], α′0 [±½], s.t. (x′, y′)=r(Y′+α′w(Y′)r^(⊥)(Y′).We can now define ϕ:R→|² to be ϕ(x′, y′)=(Y′, α′), where (Y′, α′) arethe unique values that satisfy (x′, y′)=r(Y′)+α′w(Y′)r^(⊥)(Y′).

This definition captures the notion of a “lateral maneuver” in lane'scoordinate system. Consider, for example, a widening lane, with a cardriving exactly on one of the lane's boundaries (see FIG. 23 ). Thewidening of lane 2301 means that the car 2303 is moving away from thecenter of the lane, and therefore has lateral velocity with respect tothe lane. However, this doesn't mean it performs a lateral maneuver. Thedefinition of ϕ(x′, y′)_(x)=α′, namely, the lateral distance to thelane's center in w(Y′)-units, implies that the lane boundaries have afixed lateral position of ±½. Hence, a car that sticks to one of thelane's boundaries is not considered to perform any lateral movement.Finally, it can be seen that ϕ is a homomorphism. The term lane-basedcoordinate system is used when discussing ϕ(R)=[Y_(min), Y_(max)]×[±½].We have thus obtained a reduction from a general lane geometry to astraight, longitudinal/lateral, coordinate system.

Extending RSS to General Road Structure

In this section a complete definition of RSS that holds for all roadstructures is described. This section deals with the definition of RSSand not on how to efficiently ensure that a policy adheres to RSS. Theconcept of route priority is next introduced to capture any situation inwhich more than a single lane geometry exists, for example junctions.

The second generalization deals with two-way roads, in which there canbe two cars driving at opposite directions. For this case, the alreadyestablished RSS definition is still valid, with the minor generalizationof “safe distance” to oncoming traffic. Controlled junctions (that usetraffic lights to dictate the flow of traffic), may be fully handled bythe concepts of route priority and two-way roads. Unstructured roads(for example parking areas), Where there is no clear route definitionmay also be handled with RSS. RSS is still valid for this case, wherethe only needed modification is a way to define virtual routes and toassign each car to (possibly several) routes.

Route Priority

The concept of route priority is now introduced to deal with scenariosin which there are multiple different road geometries in one scene thatoverlap in a certain area. Examples, as shown in FIGS. 24A-D, includeroundabouts, junctions, and merge into highways. A way to transformgeneral lane geometry into a lane-based one, with coherent meaning forlongitudinal and lateral axes, has been described. Now scenarios inwhich multiple routes of different road geometry exists are addressed.It follows that when two vehicles approach the overlap area, bothperform a cut-in to the frontal corridor of the other one. Thisphenomenon cannot happen when two routes have the same geometry (as isthe case of two adjacent highway lanes). Roughly speaking, the principleof route priority states that if routes r₁, r₂ overlap, and r₁ haspriority over r₂, then a vehicle coming from r₁ that enters into thefrontal corridor of a vehicle that comes from r₂ is not considered toperform a cut-in.

To explain the concept formally, recall that the blame of an accidentdepends on geometrical properties which are derived from the lane'scoordinate system, and on worst case assumptions which rely on it too.Let r₁, . . . , r_(k) be the routes defining the road's structure. As asimple example, consider the merge scenario, as depicted in FIG. 24A.Assume two cars, 2401 (c₁) and 2402 (c₂) are driving on routes r₁, r₂respectively, and r₁ is the prioritized route. For example, suppose thatr₁ is a highway lane and r₂ is a merging lane. Having defined theroute-based coordinate systems for each route, a first observation isthat we can consider any maneuver in any route's coordinate system. Forexample, if we use r₂'s coordinate system, driving straight on r₁ seemslike a merge into n's left side. One approach to definition of RSS couldbe that each of the cars can perform a maneuver IFF ∀i 0 {1, 2}, if itis safe with respect to r₂. However, this implies that c₁, driving onthe prioritized route, should be very conservative w.r.t. r₂, themerging route, as c₂ can drive exactly on the route, and hence can winby lateral position. This is unnatural, as cars on the highway have theright-of-way in this case. To overcome this problem, we define certainareas in which route priority is defined, and only some of the routesare considered as relevant for safety.

Definition 22 (Accident Responsibility with Route Priority) Suppose r₁,r₂ are two routes with different geometry that overlap. We user₁>_([b,e]) r₂ to symbolize that r₁ has priority over r₂ in thelongitudinal interval [b, e] (FIG. 25 ) of r₁ coordinate system. Supposethere is an accident between cars c₁, c₂, driving on routes r₁, r₂. Fori 0 {1,2}, let b_(i)⊂{1,2} indicate the cars to blame for the accidentif we consider the coordinate system of r_(i). The blame for theaccident is as follows:

If r₁=_([b,e]) r₂ and on the blame time w.r.t. r₁, one of the cars wasin the interval [b, e] of the r₁-system's longitudinal axis, then theblame is according to b₁.

Otherwise, the blame is according to b₁∪b2.

To illustrate the definition, consider again the merge into highwayexample. The lines denoted. “b” and “e” in FIG. 25 indicate the valuesof b, e for which r₁>_([b,e]) r₂. Thus, we allow cars to drive naturallyon the highway, while implying merging cars must be safe with respect tothose cars. In particular, observe that in the case a car 2401 c₁ drivesat the center of the prioritized lane, with no lateral velocity, it willnot be blamed for an accident with a car 2402 c₂ driving on anon-prioritized lane, unless 2402 c₂ has cut-in into 2401 c₁'s corridorat a safe distance. Note, that the end result is very similar to theregular RSS—this is exactly the same as a case where a car, on astraight road, tries to perform a lane change. Note that there may becases where the route used by another agent is unknown. For example, inFIG. 26 , car 2601 may not be able to determine whether a car 2602 willtake path “a” or path “b”, In such cases, RSS may be obtained byiteratively checking all possibilities,

Two-Way Traffic

To deal with two-way traffic, the modification to the blame definitioncomes through sharpening the parts which rely on rear/frontrelationships, as those are of a slightly different meaning in suchcases. Consider two cars c₁, c₂ driving on some straight two lane road,in opposite longitudinal directions, namely, v_(1,long)·v_(2,long)<0.The direction of driving with respect to a lane may be negative inreasonable urban scenarios, such as a car deviating to the opposite laneto overtake a parked truck, or a car reversing into a parking spot. Itis therefore required to extend the definition of the safe longitudinaldistance Which we have introduced for cases Where negative longitudinalvelocity was assumed to be un-realistic. Recall that a distance betweenc_(r), c_(f) was safe if a maximal brake by c_(f) would allow enough ofresponse time for c_(r) to brake before crashing into c_(f). In ourcase, we again consider the “worst-case” by the opposite car, in aslightly different manner: of course we do not assume that the “worstcase” is that it speeds up towards us, but that it indeed will brake toavoid a crash—but only using some reasonable braking power. In order tocapture the difference in responsibility between the cars, when one ofthem clearly drives at the opposite direction, we start by defining a“correct” driving direction.

In the RSS definition for parallel lanes, the relevant lane has beendefined as the one whose center is closest to the cut-in position. Wecan now reduce ourselves to consideration of this lane (or, in the caseof symmetry, deal with the two lanes separately, as in Definition 22).In the definition below, the term “heading” denotes the arc tangent (inradians) of the lateral velocity divided by the longitudinal velocity.

Definition 23 ((μ₁, μ₂, μ₃)-Winning by Correct Driving Direction) Assumec₁, c₂ are driving in opposite directions, namelyv_(1,long)·v_(2,long)<0. Let x_(i),h_(i) be their lateral positions andheadings w.r.t. the lane. We say that c₁ (μ₁, μ₂, μ₃)-Wins by CorrectDriving Direction if all of the following conditions hold:|h ₁|<μ₁,|h ₂−π|<μ₂,|x ₁|<μ₃.

The indicator of this event is denoted by W_(CDD)(i).

In words, c₁ wins if it drives close to the lane canter, in the correctdirection, while c₂ takes the opposite direction. At most one car canwin, and it can be that none of the cars does so. Intuitively, assumethere is a crash in the discussed situation. It is reasonable to putmore responsibility over a car c₁, that loses by Correct DrivingDirection. This is done by re-defining a_(max,brake) for the case that acar wins by correct driving direction.

Definition 24 (Reasonable Braking Power) Let a_(max,brake,wedd)>0 be aconstant, smaller than a_(max,brake). Assume c₁, c₂ are driving inopposite directions. The Reasonable Braking Power of each car c_(i),denoted RBP_(i) is a_(max,brake,wedd) if c_(i)(μ₁, μ₂, μ₃)-Wins byCorrect Driving Direction and a_(max,brake) otherwise.

The exact values of a_(max,brake,wedd), a_(max,brake), for the cases ofwinning/not-winning by correct driving direction, are constants whichshould be defined, and can depend on the type of road and the lanesdriven by each car. For example, in a narrow urban street, it may be thecase that winning by a correct driving direction does not imply a muchlesser brake value: in dense traffic, we do expect a car to brake atsimilar forces, either when someone clearly deviated into its lane ornot. However, consider an example of a rural two way road, where highspeeds are allowed. When deviating to the opposite lane, cars whichdrive at the correct direction cannot be expected to apply a very strongbraking power to avoid hitting the host vehicle—the host vehicle willhave more responsibility than them. Different constants can be definedfor the case when two cars are at the same lane, with one of themreversing into a parking spot.

The safety distance between cars which are driving in oppositedirections, and immediately derive its exact value, is next defined.

Definition 25 (Safe Longitudinal Distance—Two-Way Traffic) Alongitudinal distance between a car c₁ and another car c₂ which aredriving in opposite directions and are both in the frontal corridors ofeach other, is safe w.r.t. a response time p if any acceleration commanda, |a|<a_(max,accel), performed by c₁, c₂ until time ρ if c₁ and c₂ willapply their Reasonable Braking Power from time ρ until a full stop thenthey won't collide.

Lemma 10 Let c₁, c₂ as in Definition 25. Let RBP_(i), a_(max,accel) bethe reasonable braking (for each i) and acceleration commands, and let ρbe the cars' response time. Let v₁, v₂ be the longitudinal velocities ofthe cars, and let l₁, l₂ be their lengths. Definev_(i,p,max)=|v_(i)|+ρ·a_(max,accel) Let L=(l_(r), l_(f))/2. Then, theminimal safe longitudinal distance is:

$d_{\min} = {L + {\sum\limits_{i = 1}^{2}( {{\frac{{❘v_{i}❘} + v_{i,\rho,\max}}{2}\rho} + \frac{v_{i,\rho,\max}^{2}}{2{RBP}_{i}}} )}}$

It can be seen that the term in the sum is the maximal distancetravelled by each car until it reaches full stop, when performing themaneuver from Definition 25. Therefore, in order for the full stop to beat a distance greater than L, the initial distance must be larger thanthis sum and an additional term of L.

The same blame time definition of RSS, with the non-safe longitudinaldistance as defined in Definition 25, is used to define theblame/accident responsibility for a two-way traffic scenario.

Definition 26 (Blame in Two-Way Traffic) The Blame in Two-Way Traffic ofan accident between cars c₁, c₂ driving in opposite directions, is afunction of the state at the Blame Time, and is defined as follows:

-   -   If the Blame Time is also a cut-in time, the blame is defined as        in the regular RSS definition.    -   Otherwise, for every i, the blame is on c_(i) if at some t that        happens after the blame time, c_(i) was not braking at a power        of at least RBP_(i).

For example, assume a safe cut-in occurred before the blame time. Forexample, c₁ has deviated to the opposite lane, performed a cut-in intoc₂'s corridor, at a safe distance. Note that c₂ wins by correct drivingdirection, and hence this distance can be very large—we do not expect c₂to perform strong braking power, but only the Reasonable Braking Power.Then, both cars have responsibility not to crash into each other.However, if the cut-in was not in a safe-distance, we use the regulardefinition, noting that c₂ will not be blamed if it drove in the centerof its lane, without lateral movement. The blame will be solely on c₁.This allows a car to drive naturally at the center of its lane, withoutworrying about traffic which may unsafely deviate into its corridor. Onthe other hand, safe deviation to the opposite lane, a common maneuverrequired in dense urban traffic, is allowed, Considering the example ofa car which initiates a reverse parking maneuver, it should startreversing while making sure the distance to cars behind it is safe.

Traffic Lights

In scenarios that include intersections with traffic lights, one mightthink that the simple rule for traffic lights scenarios is “if one car'sroute has the green light and the other car's route has a red light,then the blame is on the one whose route has the red light”. However,this is not the correct rule, especially in all cases. Consider forexample the scenario depicted in FIG. 27 . Even if the car 2701 is on aroute having a green light, we do not expect it to ignore car 2703 thatis already in the intersection. The correct rule is that the route thathas a green light has priority over routes that have a red light.Therefore, we obtain clear reduction from traffic lights to the routepriority concept we have described previously.

Unstructured Road

Turning to roads where no clear route geometry can be defined, considerfirst a scenario where there is no lane structure at all (e.g. a parkinglot). A way to ensure that there will be no accidents can be to requirethat every car will drive in a straight line, while if a change ofheading occurs, it must be done when there are no close cars in mysurrounding. The rationale behind this is that a car can predict whatother cars will do, and behave accordingly. If other cars deviate fromthis prediction (by changing heading), it is done with a long enoughdistance and therefore there may be enough time to correct theprediction. When there is lane structure, it may enable smarterpredictions on What other cars will do. If there is no lane structure atall, a car will continue according to its current heading. Technicallyspeaking, this is equivalent to assigning every car to a virtualstraight route according to its heading. Next, consider the scenario ina large unstructured roundabout (e.g., around the Arc de Triomphe inParis). Here, a sensible prediction is to assume that a car willcontinue according to the geometry of the roundabout, while keeping itsoffset. Technically, this is equivalent to assigning every car to avirtual arc route according to its current offset from the center of theroundabout.

The above described driving policy system (e.g., the RL system) may beimplemented together with one or more of the described accidentliability rules to provide a navigational system that takes into accountpotential accident liability when deciding on a particular navigationalinstruction to implement. Such rules may be applied during the planningphase; e.g., within a set of programmed instructions or within a trainedmodel such that a proposed navigational action is developed by thesystem already in compliance with the rules. For example, a drivingpolicy module may account for or be trained with, for example, one ormore navigational rules upon which RSS is based. Additionally oralternatively, the RSS safety constraint may be applied as a filterlayer through which all proposed navigational actions proposed by theplanning phase are tested against the relevant accident liability rulesto ensure that the proposed navigational actions are in compliance. If aparticular action is in compliance with the RSS safety constraint, itmay be implemented. Otherwise, if the proposed navigational action isnot in compliance with the RSS safety constraint (e.g., if the proposedaction could result in accident liability to the host vehicle based onone or more of the above-described rules), then the action is not taken.

In practice, a particular implementation may include a navigation systemfor a host vehicle. The host vehicle may be equipped with an imagecapture device (e.g., one or more cameras such as any of those describedabove) that, during operation, captures images representative of anenvironment of the host vehicle. Using the image information, a drivingpolicy may take in a plurality of inputs and output a plannednavigational action for accomplishing a navigational goal of the hostvehicle. The driving policy may include a set of programmedinstructions, a trained network, etc., that may receive various inputs(e.g., images from one or more cameras showing the surroundings of thehost vehicle, including target vehicles, roads, objects, pedestrians,etc.; output from LIDAR or RADAR systems; outputs from speed sensors,suspension sensors, etc.; information representing one or more goals ofthe host vehicle—e.g., a navigational plan for delivering a passenger toa particular location, etc.). Based on the input, the processor mayidentify a target vehicle in the environment of the host vehicle, e.g.,by analyzing camera images, LIDAR output, RADAR output, etc. In someembodiments, the processor may identify a target vehicle in theenvironment of the host vehicle by analyzing one or more inputs, such asone or more camera images, LIDAR output, and/or RADAR output. Further,in some embodiments, the processor may identify a target vehicle in theenvironment of the host vehicle based on an agreement of a majority orcombination of sensor inputs (e.g., by analyzing one or more cameraimages, LIDAR output, and/or RADAR output, and receiving a detectionresult identifying the target vehicle based on a majority agreement orcombination of the inputs).

Based on the information available to the driving policy module, anoutput may be provided in the form of one or more planned navigationalactions for accomplishing a navigational goal of the host vehicle. Insome embodiments, the RSS safety constraint may be applied as a filterof the planned navigational actions. That is, the planned navigationalaction, once developed, can be tested against at least one accidentliability rule (e.g., any of the accident liability rules discussedabove) for determining potential accident liability for the host vehiclerelative to the identified target vehicle. And, as noted, if the test ofthe planned navigational action against the at least one accidentliability rule indicates that potential accident liability may exist forthe host vehicle if the planned navigational action is taken, then theprocessor may cause the host vehicle not to implement the plannednavigational action. On the other hand, if the test of the plannednavigational action against the at least one accident liability ruleindicates that no accident liability would result for the host vehicleif the planned navigational action is taken, then the processor maycause the host vehicle to implement the planned navigational action.

In some embodiments, the system may test a plurality of potentialnavigational actions against the at least one accident liability rule.Based on the results of the test, the system may filter the potentialnavigational actions to a subset of the plurality of potentialnavigational actions. For example, in some embodiments, the subset mayinclude only the potential navigational actions for which the testagainst the at least one accident liability rule indicates that noaccident liability would result for the host vehicle if the potentialnavigational actions were taken. The system may then score and/orprioritize the potential navigational actions without accident liabilityand select one of the navigational actions to implement based on, forexample, an optimized score, or a highest priority. The score and/orpriority may be based, for example, one or more factors, such as thepotential navigational action viewed as being the most safe, mostefficient, the most comfortable to passengers, etc.

In some instances, the determination of whether to implement aparticular planned navigational action may also depend on whether adefault emergency procedure would be available in a next state followingthe planned action. If a DEP is available, the RSS filter may approvethe planned action. On the other hand, if a DEP would not be available,the next state may be deemed an unsafe one, and the planned navigationalaction may be rejected. In some embodiments, the planned navigationalaction may include at least one default emergency procedure.

One benefit of the described system is that to ensure safe actions bythe vehicle, only the host vehicle's actions relative to a particulartarget vehicle need be considered. Thus, where more than one targetvehicle is present, the planned action for the host vehicle may betested tier an accident liability rule sequentially with respect to thetarget vehicles in an influence zone in the vicinity of the host vehicle(e.g., within 25 meters, 50 meters, 100 meters, 200 meters, etc.). Inpractice, the at least one processor may be further programmed to:identify, based on analysis of the at least one image representative ofan environment of the host vehicle (or based on LIDAR or RADARinformation, etc.), a plurality of other target vehicles in theenvironment of the host vehicle and repeat the test of the plannednavigational action against at least one accident liability rule fordetermining potential accident liability for the host vehicle relativeto each of the plurality of other target vehicles. If the repeated testsof the planned navigational action against the at least one accidentliability rule indicate that potential accident liability may exist forthe host vehicle if the planned navigational action is taken, then theprocessor may cause the host vehicle not to implement the plannednavigational action. If the repeated tests of the planned navigationalaction against the at least one accident liability rule indicate that noaccident liability would result for the host vehicle if the plannednavigational action is taken, then the processor may cause the hostvehicle to implement the planned navigational action.

As noted, any of the rules described above can be used as the basis forthe RSS safety test. In some embodiments, the at least one accidentliability rule includes a following rule defining a distance behind theidentified target vehicle within which the host vehicle may not proceedwithout a potential for accident liability. In other cases, the at leastone accident liability rule includes a leading rule defining a distanceforward of the identified target vehicle within which the host vehiclemay not proceed without a potential for accident liability.

While the system described above can apply the RSS safety test to asingle planned navigational action to test compliance with the rule thatthe host vehicle should not take any action for which it would be liablefor a resulting accident, the test may be applied to more than oneplanned navigational action. For example, in some embodiments, the atleast one processor, based on application of at least one driving policymay determine two or more planned navigational actions for accomplishinga navigational goal of the host vehicle. In these situations, theprocessor may test each of the two or more planned navigational actionsagainst at least one accident liability rule for determining potentialaccident liability. And, for each of the two or more plannednavigational actions, if the test indicates that potential accidentliability may exist for the host vehicle if a particular one of the twoor more planned navigational actions is taken, the processor may causethe host vehicle not to implement the particular one of the plannednavigational actions. On the other hand, for each of the two or moreplanned navigational actions, if the test indicates that no accidentliability would result for the host vehicle if a particular one of thetwo or more planned navigational actions is taken, then the processormay identify the particular one of the two or more planned navigationalactions as a viable candidate for implementation. Next, the processormay select a navigational action to be taken from among the viablecandidates for implementation based on at least one cost function andcause the host vehicle to implement the selected navigational action.

Because an implementation of RSS relates to a determination of relativepotential liability for accidents between the host vehicle and one ormore target vehicles, along with testing planned navigational actionsfor safety compliance, the system may track accident liability potentialfor encountered vehicles. For example, not only may the system be ableto avoid taking an action for which a resulting accident would result inliability to the host vehicle, but the host vehicle systems may also beable to track one or more target vehicles and identify and track whichaccident liability rules have been broken by those target vehicles. Insome embodiments, an accident liability tracking system for a hostvehicle may include at least one processing device programmed toreceive, from an image capture device, at least one image representativeof an environment of the host vehicle and analyze the at least one imageto identify a target vehicle in the environment of the host vehicle.Based on analysis of the at least one image, the processor may includeprogramming to determine one or more characteristics of a navigationalstate of the identified target vehicle. The navigational state mayinclude various operational characteristics of the target vehicle, suchas vehicle speed, proximity to a center of a lane, lateral velocity,direction of travel, distance from the host vehicle, heading, or anyother parameter that may be used to determine potential accidentliability based on any of the rules described above. The processor maycompare the determined one or more characteristics of the navigationalstate of the identified target vehicle to at least one accidentliability rule (e.g., any of the rules described above, such as winningby lateral velocity, directional priority, winning by proximity to lanecenter, following or leading distance and cut-in, etc.). Based oncomparison of the state to one or more rules, the processor may store atleast one value indicative of potential accident liability on the partof the identified target vehicle. And in the case of an accident, theprocessor may provide an output of the stored at least one value (e.g.,via any suitable data interface, either wired or wireless). Such anoutput may be provided, for example, after an accident between the hostvehicle and at least one target vehicle, and the output may be used foror may otherwise provide an indication of liability for the accident.

The at least one value indicative of potential accident liability may bestored at any suitable time and under any suitable conditions. In someembodiments, the at least one processing device may assign and store acollision liability value for the identified target vehicle if it isdetermined that the host vehicle cannot avoid a collision with theidentified target vehicle.

The accident liability tracking capability is not limited to a singletarget vehicle, but rather can be used to track potential accidentliability for a plurality of encountered target vehicles. For example,the at least one processing device may be programmed to detect aplurality of target vehicles in the environment of the host vehicle,determine navigational state characteristics for each of the pluralityof target vehicles, and determine and store values indicative ofpotential accident liability on the part of respective ones of theplurality of target vehicles based on comparisons of the respectivenavigational state characteristics for each of the target vehicles tothe at least one accident liability rule. As noted, the accidentliability rules used as the basis for liability tracking may include anyof the rules described above or any other suitable rule. For example,the at least one accident liability rule may include a lateral velocityrule, a lateral position rule, a driving direction priority rule, atraffic light-based rule, a traffic sign-based rule, a route priorityrule, etc. The accident liability tracking function may also be coupledwith safe navigation based on RSS considerations (e.g., whether anyaction of the host vehicle would result in potential liability for aresulting accident).

In addition to navigating based on accident liability considerationsaccording to RSS, navigation can also be considered in terms of vehiclenavigational states and a determination of whether a particular, futurenavigational state is deemed safe (e.g., whether a DEP exists such thataccidents may be avoided or any resulting accident will not be deemedthe fault of the host vehicle, as described in detail above). The hostvehicle can be controlled to navigate from safe state to safe state. Forexample, in any particular state, the driving policy may be used togenerate one or more planned navigational actions, and those actions maybe tested by determining if the predicted future states corresponding toeach planned action would offer a DEP, If so, the planned navigationalaction or actions providing the DEP may be deemed safe and may qualifyfor implementation.

In some embodiments, a navigation system for a host vehicle may includeat least one processing device programmed to: receive, from an imagecapture device, at least one image representative of an environment ofthe host vehicle; determine, based on at least one driving policy, aplanned navigational action for accomplishing a navigational goal of thehost vehicle; analyze the at least one image to identify a targetvehicle in the environment of the host vehicle; test the plannednavigational action against at least one accident liability rule fordetermining potential accident liability for the host vehicle relativeto the identified target vehicle; if the test of the plannednavigational action against the at least one accident liability ruleindicates that potential accident liability may exists for the hostvehicle if the planned navigational action is taken, then cause the hostvehicle not to implement the planned navigational action; and if thetest of the planned navigational action against the at least oneaccident liability rule indicates that no accident liability wouldresult for the host vehicle if the planned navigational action is taken,then cause the host vehicle to implement the planned navigationalaction.

In some embodiments, a navigation system for a host vehicle, may includeat least one processing device programmed to: receive, from an imagecapture device, at least one image representative of an environment ofthe host vehicle; determine, based on at least one driving policy, aplurality of potential navigational actions for the host vehicle;analyze the at least one image to identify a target vehicle in theenvironment of the host vehicle; test the plurality of potentialnavigational actions against at least one accident liability rule fordetermining potential accident liability for the host vehicle relativeto the identified target vehicle; select one of the potentialnavigational actions for which the test indicates that no accidentliability would result for the host vehicle if the selected potentialnavigational action is taken; and cause the host vehicle to implementthe selected potential navigational action. In some instances, theselected potential navigational action may be selected from a subset ofthe plurality of potential navigational actions for which the testindicates that no accident liability would result for the host vehicleif any of the subset of the plurality of potential navigational actionwere taken. Further, in some instances, the selected potentialnavigational action may be selected according to a scoring parameter.

In some embodiments, a system for navigating a host vehicle may includeat least one processing device programmed to receive, from an imagecapture device, at least one image representative of an environment ofthe host vehicle and determine, based on at least one driving policy, aplanned navigational action for accomplishing a navigational goal of thehost vehicle. The processor may also analyze the at least one image toidentify a target vehicle in the environment of the host vehicle;determine a next-state distance between the host vehicle and the targetvehicle that would result if the planned navigational action was taken;determine a current maximum braking capability of the host vehicle and acurrent speed of the host vehicle; determine a current speed of thetarget vehicle and assume a maximum braking capability of the targetvehicle based on at least one recognized characteristic of the targetvehicle; and implement the planned navigational action if, given themaximum braking capability of the host vehicle and current speed of thehost vehicle, the host vehicle can be stopped within a stopping distancethat is less than the determined next-state distance summed togetherwith a target vehicle travel distance determined based on the currentspeed of the target vehicle and the assumed maximum braking capabilityof the target vehicle. The stopping distance may further include adistance over which the host vehicle travels during a reaction timewithout braking.

The recognized characteristic of the target vehicle upon which themaximum braking capability of the target vehicle is determined mayinclude any suitable characteristic. In some embodiments, thecharacteristic may include a vehicle type (e.g., motorcycle, car, bus,truck, each of which may be associated with different braking profiles),vehicle size, a predicted or known vehicle weight, a vehicle model(e.g., that may be used to look up a known braking capability), etc.

In some cases, the safe state determination may be made relative to morethan one target vehicle. For example, in some cases a safe statedetermination (based on distance and braking capabilities) may be basedon two or more identified target vehicles leading a host vehicle. Such adetermination may be useful especially where information regarding whatis ahead of the foremost target vehicle is not available. In such cases,it may be assumed for purposes of determining a safe state, safedistance, and/or available DEP that the foremost detectable vehicle willexperience an imminent collision with an immovable or nearly immovableObstacle, such that the target vehicle following may reach a stop morequickly than its own braking profile allows (e.g., the second targetvehicle may collide with a first, foremost vehicle and therefore reach astop more quickly than expected max braking conditions). In such cases,it may be important to base the safe state, safe following distance, DEPdetermination upon the location of the foremost identified targetvehicle relative to the host vehicle.

In some embodiments, such a safe state to safe state navigation systemmay include at least one processing device programmed to receive, froman image capture device, at least one image representative of anenvironment of the host vehicle. Here, as with other embodiments, theimage information captured by an image capture device (e.g., a camera)may be supplemented with information obtained from one or more othersensors, such as a LIDAR or RADAR system. In some embodiments, the imageinformation used to navigate may even originate from a LIDAR or RADARsystem, rather than from an optical camera. The at least one processormay determine, based on at least one driving policy, a plannednavigational action for accomplishing a navigational goal of the hostvehicle. The processor may analyze the at least one image (e.g.,obtained from any of a camera, a RADAR, a LIDAR, or any other devicefrom which an image of the environment of the host vehicle may beObtained, whether optically based, distance map-based, etc.) to identifya first target vehicle ahead of the host vehicle and a second targetvehicle ahead of the first target vehicle. The processor may thendetermine a next-state distance between the host vehicle and the secondtarget vehicle that would result if the planned navigational action wastaken. Next, the processor may determine a current maximum brakingcapability of the host vehicle and a current speed of the host vehicle.The processor may implement the planned navigational action if, giventhe maximum braking capability of the host vehicle and the current speedof the host vehicle, the host vehicle can be stopped within a stoppingdistance that is less than the determined next-state distance betweenthe host vehicle and the second target vehicle.

That is, if the host vehicle processor determines that there is enoughdistance to stop in a next-state distance between the leading visibletarget vehicle and the host vehicle, without collision or withoutcollision for which responsibility would attach to the host vehicle andassuming the leading visible target vehicle will suddenly at any momentcome to a complete stop, then the processor of the host vehicle may takethe planned navigational action. On the other hand, if there would beinsufficient room to stop the host vehicle without collision, then theplanned navigational action may not be taken.

Additionally, while the next-state distance may be used as a benchmarkin some embodiments, in other cases, a different distance value may beused to determine whether to take the planned navigational action. Insome cases, as in the one described above, the actual distance in whichthe host vehicle may need to be stopped to avoid a collision may be lessthan the predicted next-state distance. For example, where the leading,visible target vehicle is followed by one or more other vehicles (e.g.,the first target vehicle in the example above), the actual predictedrequired stopping distance would be the predicted next-state distanceless the length of the target vehicle(s) following the leading visibletarget vehicle. If the leading visible target vehicle comes to animmediate stop, it may be assumed that the following target vehicleswould collide with the leading visible target vehicle and, therefore,they too would need to be avoided by the host vehicle to avoid acollision. Thus, the host vehicle processor can evaluate the next-statedistance less the summed lengths of any intervening target vehiclesbetween the host vehicle and the leading, visible/detected targetvehicle to determine whether there would be sufficient space to bringthe host vehicle to a halt under max braking conditions without acollision.

In other embodiments, the benchmark distance for evaluating a collisionbetween the host vehicle and one or more leading target vehicles may begreater than the predicted next-state distance. For example, in somecases, the leading visible/detected target vehicle may come to a quick,but not immediate stop, such that the leading visible/detected targetvehicle travels a short distance after the assumed collision. Forexample, if that vehicle hits a parked car, the colliding vehicle maystill travel some distance before coming to a complete stop. Thedistance traveled after the assumed collision may be less than anassumed or determined minimum stopping distance for the relevant targetvehicle. Thus, in some cases, the processor of the host vehicle maylengthen the next-state distance in its evaluation of whether to takethe planned navigational action. For example, in this determination, thenext-state distance may be increased by 5%, 10%, 20%, etc. or may besupplemented with a predetermined fixed distance (10 m, 20 m, 50 m,etc.) to account for a reasonable distance that the leading/visibletarget vehicle may travel after an assumed imminent collision.

In addition to lengthening the next-state distance in the evaluation byan assumed distance value, the next-state distance may be modified byboth accounting for a distance traveled after collision by the leadingvisible/detected target vehicle and the lengths of any target vehiclesfollowing the leading visible/detected target vehicle (which may beassumed to pile up with the leading visible/detected vehicle after itssudden stop).

In addition to basing the determination on whether to take the plannednavigational action on the next-state distance between the host vehicleand the leading visible/detected target vehicle (as modified byconsidering the post-collision movement of the leading visible/detectedtarget vehicle and/or the lengths of vehicles following the leadingvisible/detected target vehicle), the host vehicle may continue toaccount for the braking capability of one or more leading vehicles inits determination. For example, the host vehicle processor may continueto determine a next-state distance between the host vehicle and thefirst target vehicle (e.g., a target vehicle following the leadingvisible/detected target vehicle) that would result if the plannednavigational action was taken; determine a current speed of the firsttarget vehicle and assume a maximum braking capability of the firsttarget vehicle based on at least one recognized characteristic of thefirst target vehicle; and not implement the planned navigational actionif, given the maximum braking capability of the host vehicle and thecurrent speed of the host vehicle, the host vehicle cannot be stoppedwithin a stopping distance that is less than the determined next-statedistance between the host vehicle and the first target vehicle summedtogether with a first target vehicle travel distance determined based onthe current speed of the first target vehicle and the assumed maximumbraking capability of the first target vehicle. Here, as in the examplesdescribed above, the recognized characteristic of the first targetvehicle may include a vehicle type, a vehicle size, a vehicle model,etc.

In some cases (e.g., through actions of other vehicles), the hostvehicle may determine that a collision is imminent and unavoidable. Insuch cases, the processor of the host vehicle may be configured toselect a navigational action (if available) for which the resultingcollision would result in no liability to the host vehicle. Additionallyor alternatively, the processor of the host vehicle may be configured toselect a navigational action that would offer less potential damage tothe host vehicle or less potential damage to a target object than thecurrent trajectory or relative to one or more other navigationaloptions. Further, in some cases, the host vehicle processor may select anavigational action based on considerations of the type of object orobjects for which a collision is expected. For example, when faced witha collision with a parked car for a first navigational action or with animmovable object for a second navigational action, the action offeringthe lower potential damage to the host vehicle (e.g., the actionresulting in a collision with the parked car) may be selected. Whenfaced with a collision with a car moving in a similar direction as thehost vehicle for a first navigational action or with a parked car for asecond navigational action, the action offering the lower potentialdamage to the host vehicle (e.g., the action resulting in a collisionwith the moving car) may be selected. When faced with a collision with apedestrian as a result of a first navigational action or with any otherobject for a second navigational action, the action offering anyalternative to colliding with a pedestrian may be selected.

In practice, the system for navigating a host vehicle may include atleast one processing device programmed to receive, from an image capturedevice, at least one image representative of an environment of the hostvehicle (e.g., a visible image, LIDAR image, RADAR image, etc.); receivefrom at least one sensor an indicator of a current navigational state ofthe host vehicle; and determine, based on analysis of the at least oneimage and based on the indicator of the current navigational state ofthe host vehicle, that a collision between the host vehicle and one ormore objects is unavoidable. The processor may evaluate availablealternatives. For example, the processor may determine, based on atleast one driving policy, a first planned navigational action for thehost vehicle involving an expected collision with a first object and asecond planned navigational action for the host vehicle involving anexpected collision with a second object. The first and second plannednavigational actions may be tested against at least one accidentliability rule for determining potential accident liability. If the testof the first planned navigational action against the at least oneaccident liability rule indicates that potential accident liability mayexist for the host vehicle if the first planned navigational action istaken, then the processor may cause the host vehicle not to implementthe first planned navigational action. If the test of the second plannednavigational action against the at least one accident liability ruleindicates that no accident liability would result for the host vehicleif the second planned navigational action is taken, then the processormay cause the host vehicle to implement the second planned navigationalaction. The objects may include other vehicles or non-vehicle objects(e.g., road debris, trees, poles, signs, pedestrians, etc.).

The following figures and discussion provide examples of variousscenarios that may occur when navigating and implementing the disclosedsystems and methods. In these examples, a host vehicle may avoid takingan action that would result in blame attributable to the host vehiclefor a resulting accident if the action is taken.

FIGS. 28A and 28B illustrate example following scenarios and rules. Asshown in FIG. 28A, the region surrounding vehicle 2804 (e.g., a targetvehicle) represents a minimum safe distance corridor for vehicle 2802(e.g., a host vehicle), which is traveling in the lane a distance behindvehicle 2804. According to one rule consistent with disclosedembodiments, to avoid an accident in which blame is attributable tovehicle 2802, vehicle 2802 must maintain a minimum safe distance byremaining in the region surrounding vehicle 2802. In contrast, as shownin FIG. 28B, if vehicle 2804 brakes, then vehicle 2802 will be at faultif there is an accident.

FIGS. 29A and 293 illustrate example blame in cut-in scenarios. In thesescenarios, safe corridors around vehicle 2902 determine the fault incut-in maneuvers. As shown in FIG. 29A, vehicle 2902 is cutting in frontof vehicle 2904, violating the safe distance (depicted by the regionsurrounding vehicle 2904) and therefore is at fault. As show in FIG.29B, vehicle 2902 is cutting in front of vehicle 2904, but maintains asafe distance in front of vehicle 2904.

FIGS. 30A and 303 illustrate example blame in cut-in scenarios. In thesescenarios, safe corridors around vehicle 3004 determine whether vehicle3002 is at fault. In FIG. 30A, vehicle 3002 is traveling behind vehicle3006 and changes into the lane in which target vehicle 3004 istraveling. In this scenario, vehicle 3002 violates a safe distance andtherefore is at fault if there is an accident. In FIG. 303 , vehicle3002 cuts in behind vehicle 3004 and maintains a safe distance.

FIGS. 31A-31D illustrate example blame in drifting scenarios. In FIG.31A, the scenario starts with a slight lateral maneuver by vehicle 3104,cutting-in to the wide corridor of vehicle 3102. In FIG. 31B, vehicle3104 continues cutting into the normal corridor of the vehicle 3102,violating a safe distance region. Vehicle 3104 is to blame if there isan accident. In FIG. 31C, vehicle 3104 maintains its initial position,while vehicle 3102 moves laterally “forcing” a violation of a normalsafe distance corridor. Vehicle 3102 is to blame if there is anaccident. In FIG. 31B, vehicle 3102 and 3104 move laterally towards eachother. The blame is shared by both vehicles if there is an accident.

FIGS. 32A and 323 illustrate example blame in two-way traffic scenarios.In FIG. 32A, vehicle 3202 overtakes vehicle 3206, and vehicle 3202 hasperformed a cut-in maneuver maintaining a safe distance from vehicle3204. If there is an accident, vehicle 3204 is to blame for not brakingwith reasonable force. In FIG. 323 , vehicle 3202 cuts-in withoutkeeping safe longitudinal distance from vehicle 3204. In case of anaccident, vehicle 3202 is to blame.

FIGS. 33A and 333 illustrate example blame in two-way traffic scenarios.In FIG. 33A, vehicle 3302 drifts into the path of oncoming vehicle 3204,maintaining a safe distance. In case of an accident, vehicle 3204 is toblame for not braking with reasonable force. In FIG. 33B, vehicle 3202drifts into the path of the oncoming vehicle 3204, violating a safelongitudinal distance. In case of an accident, vehicle 3202 is to blame.

FIGS. 34A and 34B illustrate example blame in route priority scenarios.In FIG. 34A, vehicle 3402 runs a stop sign. Blame is attributed tovehicle 3402 for not respecting the priority assigned to vehicle 3404 bythe traffic light. In FIG. 343 , although vehicle 3402 did not havepriority, it was already in the intersection when vehicle 3404's lightturned green. If vehicle 3404 hits 3402, vehicle 3404 would be to blame.

FIGS. 35A and 35B illustrate example blame in route priority scenarios.In FIG. 35A, vehicle 3502 backing-up into the path of an oncomingvehicle 3504. Vehicle 3502 performs a cut-in maneuver maintaining a safedistance. In case of an accident, vehicle 3504 is to blame for notbraking with reasonable force. In FIG. 35B, vehicle 3502 car cuts-inwithout keeping a safe longitudinal distance. In case of an accident,vehicle 3502 is to blame.

FIGS. 36A and 36B illustrate example blame in route priority scenarios.In FIG. 36A, vehicle 3602 and vehicle 3604 are driving in the samedirection, while vehicle 3602 turns left across the path of vehicle3604. Vehicle 3602 performs cut-in maneuver maintaining safe distance.In case of an accident, vehicle 3604 is to blame for not braking withreasonable force. In FIG. 36B, vehicle 3602 cuts-in without keeping safelongitudinal distance. In case of an accident, vehicle 3602 is to blame.

FIGS. 37A and 37B illustrate example blame in route priority scenarios.In FIG. 37A, vehicle 3702 wants to turn left, but must give way to theoncoming vehicle 3704. Vehicle 3702 turns left, violating safe distancewith respect to vehicle 3704. Blame is on vehicle 3702. In FIG. 37B,vehicle 3702 turns left, maintaining a safe distance with respect tovehicle 3704. In case of an accident, vehicle 3704 is to blame for notbraking with reasonable force.

FIGS. 38A and 38B illustrate example blame in route priority scenarios.In FIG. 38A, vehicle 3802 and vehicle 3804 are driving straight, andvehicle 3802 has a stop sign. Vehicle 3802 enters the intersection,violating a safe distance with respect to vehicle 3804. Blame is onvehicle 3802. In FIG. 38B, vehicle 3802 enters the intersection whilemaintaining a safe distance with respect to vehicle 3804. In case of anaccident, vehicle 3804 is to blame for not braking with reasonableforce.

FIGS. 39A and 39B illustrate example blame in route priority scenarios.In FIG. 39A, vehicle 3902 wants to turn left, but must give way tovehicle 3904 coming from its right. Vehicle 3902 enters theintersection, violating the right-of-way and a safe distance withrespect to vehicle 3904. Blame is on vehicle 3902. In FIG. 39B, vehicle3902 enters the intersection while maintaining the right-of-way and asafe distance with respect to vehicle 3904. In case of an accident,vehicle 3904 is to blame for not braking with reasonable force.

FIGS. 40A and 40B illustrate example blame in traffic light scenarios.In FIG. 40A, vehicle 4002 is running a red light. Blame is attributed tovehicle 4002 for not respecting the priority assigned to vehicle 4004 bythe traffic light. In FIG. 40B, although vehicle 4002 did not havepriority, it was already in the intersection when the light for vehicle4004 turned green. If vehicle 4004 hits vehicle 4002, vehicle 4004 wouldbe to blame.

FIGS. 41A and 41B illustrate example blame in traffic light scenarios.Vehicle 4102 is turning left across the path of the oncoming vehicle4104. Vehicle 4104 has priority. In FIG. 41 , vehicle 4102 turns left,violating a safe distance with respect to vehicle 4104. Blame isattributed to vehicle 4102. In FIG. 41B, vehicle 4102 turns left,maintaining a safe distance with respect to vehicle 4104. In case of anaccident, vehicle 4104 is to blame for not braking with reasonableforce.

FIGS. 42A and 42B illustrate example blame in traffic light scenarios.In FIG. 42A, vehicle 4202 is turning right, cutting into the path ofvehicle 4204, which is driving straight. Right-on-red is assumed to be alegal maneuver, but vehicle 4204 has right of way, as vehicle 4202violates a safe distance with respect to vehicle 4204. Blame isattributed to vehicle 4202. In FIG. 42B, vehicle 4202 turns right,maintaining a safe distance with respect to vehicle 4204. In case of anaccident, vehicle 4204 is to blame for not braking with reasonableforce.

FIGS. 43A-43C illustrate example vulnerable road users (VRUs) scenarios.

Accidents with animals or VRUs Where the vehicle performs a maneuver aretreated as a variation of a cut-in, where the default blame is on thecar, with some exceptions. In FIG. 43A, vehicle 4302 cuts into the pathof an animal (or VRU) while maintaining safe distance and ensuring anaccident can be avoided. In FIG. 43B, vehicle 4302 cuts into the path ofan animal (or VRU) violating safe distance. Blame is attributed tovehicle 4302. In FIG. 43C, vehicle 4302 notices the animal and stops,giving the animal sufficient time to stop. If the animal hits the car,the animal is to blame.

FIGS. 44A-44C illustrate example vulnerable road users (VRUs) scenarios.In FIG. 44A, vehicle 4402 is turning left at a signalized intersectionand encounters a pedestrian in the crosswalk. Vehicle 4402 has a redlight and the VRU has a green. Vehicle 4402 is at fault. In FIG. 4413 ,vehicle 4402 has a green light, and the VRU has a red light. If the VRUenters the crosswalk, the VRU is at fault. In FIG. 44C, vehicle 4402 hasa green light, and the VRU has a red light. If the VRU was already inthe crosswalk, vehicle 4402 is it fault.

FIGS. 45A-45C illustrate example vulnerable road users (VRUs) scenarios.In FIG. 45A, vehicle 4502 is turning right and encounters a cyclist. Thecyclist has a green light. Vehicle 4502 is at fault. In FIG. 45B, thecyclist has a red light. If the cyclist enters the intersection, thecyclist is at fault. In FIG. 45C, the cyclist has a red light, but wasalready in the intersection. Vehicle 4502 is at fault.

FIGS. 46A-46D illustrate example vulnerable road users (VRUs) scenarios.Accidents with VRUs where a vehicle does not perform a maneuver areblamed on the car by default, with some exceptions. In FIG. 46A, vehicle4602 must always make sure to maintain safe distance and ensuring anaccident can be avoided with a VRU, In FIG. 4613 , if vehicle 4602 doesnot maintain safe distance, vehicle 4602 is to blame. In FIG. 46C, ifvehicle 4602 does not maintain sufficiently low speed as to avoidcolliding with a VRU that is potentially occluded by vehicle 5604, ordrives above the legal limit, vehicle 4602 is to blame. In FIG. 46D,another scenario with a potential occlusion of a VRU by vehicle 4604, ifvehicle 4602 maintains sufficiently low speed, but the VRUs speed isabove a reasonable threshold, the VRU is to blame.

As disclosed herein, RSS defines a framework for multi-agent scenarios,Accidents with static objects, road departures, loss of control orvehicle failure are blamed on the host. RSS defines cautious maneuvers,which will not allow accidents with other objects, unless other objectsmaneuvers dangerously into the path of the host (in which case they areto blame). In the case of a sure-collision where blame is on the target,the host will apply its brakes. The system may consider evasive steeringonly if the maneuver is “cautious” (perceived not to cause anotheraccident).

Non-collision incidents include accidents initiated by vehicle fires,potholes, falling objects, etc. In these cases, the blame may default tothe host, except for scenarios which the host can avoid, such aspotholes and falling objects, which may be classified as a “staticobject” scenario, assuming they become visible at safe distance or thata cautious evasive maneuver exists. In multi-agent scenarios where thehost vehicle was stationary, the host is not to blame. In this case thetarget essentially performed a non-safe cut-in. For example, if acyclist rides into a stationary car, the host is not to blame.

RSS also includes guidelines for assigning blame where the road is notstructured clearly, such as parking lots or wide roundabouts withoutlane marks. In these unstructured road scenarios, blame is assigned byexamining deviations of each vehicle from its path to determine if theyallowed sufficient distance to allow other objects in the area toadjust.

Additional Details Relating to Responsibility-Sensitive Safety (RSS)

As discussed above, RSS provides a set of mathematical formulae that canbe used to guarantee that a vehicle implementing RSS will not beinvolved in an accident caused by it. As a result, in someimplementations, RSS may set an envelope of extremes (e.g., a minimumsafe longitudinal distance) that would guarantee that the vehicleimplementing RSS will not be involved in an accident for which it is toblame. In some embodiments, a system can implement a modified RSS, whichmay involve a predetermined operational envelope that that may be largerthan the RSS protocol described above. Such a modified RSS can, at leastin some circumstances, provide a heightened level of safety and reducethe probability that fault may be attributable to a vehicle employingRSS. Such a modified RSS system will be described in more detail below,for example, relating to the described comfort RSS system.

As discussed above, RSS may assume that a host vehicle will brake at itsmaximum braking capability to avoid a collision with a target vehicle, aVRU, or another object. RSS may determine a safe longitudinal distancebetween a host vehicle, effectively a buffer zone, having a size, asdescribed above, based on host and target vehicle velocities, host andtarget vehicle maximum braking capabilities, and the maximumacceleration capability of the host vehicle over a host vehicle reactiontime. If a host vehicle comes within a distance less than the safedistance (e.g., the RSS distance), then the host vehicle may not be ableto stop (at least in some cases) without contacting a target vehicle,even if braking at its maximum braking capacity, as shown in theexamples of FIGS. 28A-46D. Applying maximum braking, especially whensuch application is sudden, may be regarded as an extreme response thatshould be reserved for cases when it is not avoidable. Under certaincircumstances, maximum braking can be uncomfortable to passengers, canimplicate trailing vehicles, can excessively wear down vehicle hardware(tires, brake pads etc.), etc. Thus, to avoid maximum braking scenariosand potential contact with target vehicles, a driving policy based onthe RSS safe distance may be adopted at least under certaincircumstances or in some implementations, to maintain a safelongitudinal distance relative to target vehicles.

As noted above, an RSS distance may include a component dependent uponthe maximum possible acceleration capability that the host vehicle mayexperience during a period between a sensed event and a host vehicle'sreaction to a sensed event (i.e., a reaction time associated with thehost vehicle). For example, RSS may account for a delay between theperiod in which a target vehicle, VRU, or other object is sensed by ahost vehicle and the time the host vehicle begins applying the brake ormaking another navigational maneuver. For example, there may be severalmilliseconds (or more or less) between the time a host vehicle detectsthat a target vehicle is braking and the time the host vehicle beginsbraking or another avoidance maneuver. Further details relating to RSSand the RSS safe distance are described above.

Definition 27 (RSS safe distance) A longitudinal distance between a carc_(r) and another car c_(f) that is in c_(r) 's frontal corridor is safew.r.t. a response time p if for any braking of at most a_(max,brake),performed by c_(f), if c_(r) will accelerate by at most a_(max,accel)during the response time ρ, and from there on will brake by its maximalbrake a_(max,brake) from time ρ until a full stop then it won't collidewith c_(f).

Lemma 11 below calculates an example of an RSS safe distance accordingto this embodiment for a host vehicle following a target vehicle. TheRSS safe distance may include an assumption of the maximum brakingcapacity and determined current speed of a target vehicle.

Lemma 11 Let c_(r) be a host vehicle which is behind a target vehiclecon the longitudinal axis. Let a_(max,brake) be the maximal brakingcapacity and let a_(max,accel) be the maximum acceleration of a vehicle.Let v be a current velocity of a vehicle. Let ρ be the response time ofhost vehicle c_(r). Then, the RSS safe distance for host vehicle c_(r)is:

${RSS}_{Distance} = {\max( {{{\frac{v_{1} + ( {v_{1} + {\rho a_{\max,{accel}}}} )}{2}\rho} + \frac{( {v_{1} + {\rho a_{\max,{accell}}}} )^{2} - \nu_{2}^{2}}{2a_{\max,{brake}}}},0} )}$

Proof. The RSS safe distance may include a calculation of the minimumdistance that it would take the vehicles to stop if braking at maximumbraking capacity a_(max,brake). This minimum distance may be calculatedin any manner described above in relation to RSS and the formula used inLemma 11 is exemplary only. For example, the minimum distance needed tocome to a stop may be calculated using Lemma 2. Lemma 11 provides anexample of the modifications need to account for the acceleration thatmay occur during response period ρ. Let v₁ be the current velocity of ahost vehicle c_(r) and v₂ be the current velocity of a target vehiclec_(f). Then for host vehicle c_(r), the RSS_(Distance) includes acalculation of the velocity of host vehicle c_(r) after accelerating ata maximum acceleration capacity a_(max,accel) for the response period ρand multiplies that velocity by the response period ρ to determine amaximum distance traveled during the response period ρ. The maximumdistance traveled during response period ρ is:d _(max,ρ)=(v ₁+(v ₁ +ρa _(max,accel)))ρ

The velocity of the host vehicle used in the safe distance determinationmay correspond to a maximum possible velocity of the host vehicle afteraccelerating for its response period, ρ. For example, let v₁ be acurrent velocity of the host vehicle, let ρ be the response period, andlet a_(max,accel) be the maximum acceleration of the host vehicle, thenthe maximum possible velocity v_(max,ρ) of the host vehicle after theresponse period ρ is:v _(max,ρ) =v ₁ +ρa _(max,accel)

In some embodiments, an RSS safe distance may also include a componentto ensure that even if both the host and the target vehicles stop withmaximum braking capabilities from their current speed (and after amaximum acceleration of the host vehicle over its reaction time). Such acomponent may include a minimum distance of approach component. Theminimum distance of approach may correspond with a minimum distancecomponent in an RSS safe distance calculation such that even if the hostvehicle and the target vehicle apply maximum braking while stopping (andafter the host vehicle reaction time at maximum acceleration) the hostvehicle will stop at least the minimum distance from a sensed targetvehicle, VRU, or other object. For example, if a host vehicle istraveling behind a target vehicle and the target vehicle begins brakingat its maximum braking capacity, the host vehicle equipped with RSS mayrespond by braking at its maximum braking capacity. If RSS safe distanceincludes a minimum distance of approach component, then the host vehiclemay come to a stop at least the minimum distance from the targetvehicle. The minimum distance may be predetermined (e.g., a minimumdistance of 0.5 m, 1 m, 2 m, etc.) or may be determined based on any setof factors consistent with this disclosure (e.g., a velocity associatedwith host vehicle and/or target vehicle, a sensed weather condition, auser's preferences, etc.). The following expression for the RSS safedistance includes a minimum distance d_(min):

${RSS}_{Distance} = {{\max( {{{\frac{v_{1} + ( {v_{1} + {\rho a_{\max,{accel}}}} )}{2}\rho} + \frac{( {v_{1} + {\rho a_{\max,{accel}}}} )^{2} - \nu_{2}^{2}}{2a_{\max,{brake}}}},0} )} + d_{\min}}$

FIGS. 47A and 47B further illustrate the concept of an RSS safe distancewhen a host vehicle is traveling behind a target vehicle. For example,FIG. 47A shows an RSS safe distance 4702 between a host vehicle 4704 anda target vehicle 4706. Even in a worst-case scenario, where targetvehicle 4706 brakes at its maximum braking capability, at RSS safedistance 4702, host vehicle 4704 will be able to stop by braking at itsmaximum braking capability without colliding with target vehicle 4706,even if maximum braking commences after a response time of the hostvehicle during which it accelerates at its maximum accelerationcapability. In most instances, target vehicle 4706 may not need to braketo a complete stop at its maximum braking capability. In such instances,host vehicle 4704 may brake at its maximum braking capability until itbecomes at least RSS safe distance 4702 away from target vehicle 4706.

FIG. 47B illustrates an RSS safe distance 4722 between a host vehicle4724 and a target vehicle 4726. In this embodiment. RSS safe distance4722 includes RSS safe distance 4702 and a minimum approach distance4710. As discussed above, minimum approach distance 4710 may be aminimum separation distance that will exist between host vehicle 4724and target vehicle 4726 if they were both to brake at their maximumbraking capability and to come to a stop (even after the host vehicleaccelerates at its maximum acceleration capability over its reactiontime).

Consistent with this disclosure, a system for navigating a host vehicleis disclosed. The system may include at least one processing deviceprogrammed to perform one or more methods, processes, functions, oroperations consistent with this disclosure. In some embodiments, thesystem may be an ADAS system or another navigational system disclosedherein. Similarly, the processing device may be processing device 110 oranother processor or processing device in or in communication with ahost vehicle.

FIG. 48 is a flowchart depicting an exemplary process 4800 that may beperformed by the at least one processing device. Process 4800 isexemplary only. One of ordinary skill in the art having the benefit ofthis disclosure may understand that process 4800 may include additionalsteps, exclude certain steps, or may be otherwise modified in a mannerconsistent with this disclosure.

Process 4800 may include a step 4802 for receiving at least one imagerepresenting an environment of a host vehicle. Consistent with thisdisclosure, the at least one processing device may be programmed toreceive at least one image representative of an environment of the hostvehicle. As discussed above, the at least one image may be received froman image capture device. The image capture device may be any consistentwith this disclosure, including image capture device 122. In someembodiments, the at least one image may be an image obtained from any ofa camera, a RADAR, a LIDAR, or any other device from which an image maybe obtained, whether optical or otherwise. There may some period ofdelay between the time when the image is captured and time when theprocessing device receives the image. Further, there may a period ofdelay between the time when an event occurs and the imaging devicecaptures an image of the event. For example, if a target vehicle entersa lane in front of a host vehicle, there may be a short period (e.g., amillisecond, 2 milliseconds, 5 milliseconds, etc.) between when thetarget vehicle maneuvers into the lane and when the imaging devicecaptures an image of the target vehicle.

Process 4800 may include a step 4804 for determining a plannednavigational action for the host vehicle. Consistent with thisdisclosure, the at least one processing device may be programmed todetermine a planned navigation action for accomplishing a navigationalgoal of the host vehicle. The navigation action may be determined basedon at least one driving policy. The planned navigation action and/or theat least one driving policy may be any consistent with this disclosure,including those discussed above. For example, the planned navigationaction may include at least one of a lane change maneuver, a mergemaneuver, a passing maneuver, a follow distance reduction maneuver, or amaintain throttle action. The processing device may be programmed toanalyze the at least one image to identify a target vehicle in theenvironment of the host vehicle. The at least one image may be an imagereceived from an image capture device, such as image capture device 122.The at least one image may be the one or more images received as part ofstep 4802 of process 4800.

Process 4800 may include a step 4806 for determining a next-statedistance associated with the planned navigation action. Consistent withthis disclosure, the processing device may be programmed to determine anext-state distance between the host vehicle and the target vehicle thatwould result if the planned navigation action was taken. The next-statedistance may be calculated by any means disclosed herein, including theRSS safe distance formula above. For example, if the planned navigationaction is an acceleration of the host vehicle, the next-state distancemay be a distance between the host vehicle and a vehicle in front of thehost vehicle. In some examples, more than one next-state distance may bedetermined. For example, if the planned navigation action is a mergeinto an adjacent lane, a first next-state distance may be determined inrelation to the host vehicle and a first target vehicle that will be infront of the host vehicle after the merge and a second next-statedistance may be determined in relation to a second target vehicle thatwill be behind the host vehicle after the merge.

Process 4800 may include a step 4808 for determining a maximum brakingcapability, a maximum acceleration capability, and a current speed ofthe host vehicle. Consistent with this disclosure, the processing devicemay be programmed to determine a maximum braking capability of the hostvehicle, a maximum acceleration capability of the host vehicle, and/or aspeed of the host vehicle. Each of the factors, (i.e., the maximumbraking capability, the maximum acceleration capability, and the speedof the host vehicle) may be determined by any means consistent with thisdisclosure. In some embodiments, the maximum braking capability and/orthe maximum acceleration capability of the host vehicle may bedetermined based on, for example, the current speed of the vehicle, roadcharacteristics (e.g., a slope of the road, a material of the road,etc.), weather conditions (e.g., snowy, humid, etc.), vehicle conditions(e.g., tire pressure, brake-pad condition, current load of the vehicle,etc.), or the like. In some embodiments, one or more of the factors maybe determined based on an output of one or more sensors. For example, ahost vehicle may contain an accelerometer, which may provide an outputto the processing device, and that output may include a current speed ofthe host vehicle and/or an acceleration capacity of the host vehicle. Insome embodiments, the processing device may determine a current speed ofthe host vehicle and use the current speed to determine a currentmaximum braking capability and/or a current acceleration capability. Forexample, the maximum braking capability of vehicle traveling at a firstspeed (e.g., 15 km/hr) may be significantly different from the maximumbraking capability of the same vehicle traveling at a second speed(e.g., 30 km/hr). In some embodiments, one or more of the maximumbraking capability, the maximum acceleration capability, and/or thespeed of the host vehicle may be assumed using a predetermined value.For example, the processing device may be configured to assume that thehost vehicle has a maximum braking capability corresponding with apredetermined value corresponding with an average (or the worst) maximumbraking capability of the type of vehicle associated with the hostvehicle. In some embodiments, each factor may be determined based onexternal conditions of the road or temporary characteristics of thevehicle. For example, the maximum braking capability of the host vehiclemay be determined based on a sensed condition of a road surface. In thisexample, the sensed road condition may include a roughness of the road,a slant or slope of the road, the present or absence of a substance orobject on the road, whether the road is asphalt, cement, gravel, oranother material, or any other condition consistent with thisdisclosure. As another example, the maximum braking capability of thehost vehicle may be determined based on a sensed weather condition. Inthis example, the weather condition may include a detection of anyprecipitation (e.g., rain, sleet, snow, ice, etc.), a weather conditionthat affects visibility (e.g., fog, smog, smoke, etc.), a weathercondition that may affect the handling of the vehicle (e.g., strongwinds, high heat, etc.), or any other weather condition that may affecta navigational response of the host vehicle. In another example,processing device may determine a maximum braking capability based onwhether the host vehicle contains, for example, one passenger or aplurality of passengers, cargo of a significant weight, a trailer, etc.

In some embodiments, the maximum braking capability and/or the maximumacceleration capability may be determined based on one or morepredefined factors. For example, a government or industry entity mayprovide one or more regulations that dictate a maximum brakingcapability and/or a maximum acceleration capability that a vehicle orclass of vehicles may have and the at least one processor may assumethat that the host vehicle has the maximum braking capability and/or themaximum acceleration capability allowed by the regulations.

Process 4800 may include a step 4810 for determining a current stoppingdistance for the host vehicle. Consistent with this disclosure, theprocessing device may be configured to determine a current stoppingdistance for the host vehicle based on the current maximum brakingcapability of the host vehicle, the current maximum accelerationcapability of the host vehicle, and/or the current speed of the hostvehicle. The current stopping distance for the host vehicle may bedetermined by any means consistent with this disclosure. For example,processing device may use one or more of the formulas discussed inrelation with RSS above.

In some embodiments, a current stopping distance may be a distance thata host vehicle needs to come to a stop, given its current speed, if thehost vehicle were to accelerate at its maximum acceleration capabilityfor period of time before braking at its maximum braking capability. Forexample, the current stopping distance for the host vehicle may includean acceleration distance that corresponds to a distance the host vehiclecan travel over a predetermined time period at the current maximumacceleration capability of the host vehicle, starting from thedetermined current speed of the host vehicle. The predetermined timeperiod may be a time period assumed by the processing device. Forexample, a constraint may dictate that the processing device assumes ahost vehicle will accelerate for a certain time period (e.g., 0.5milliseconds, 1 millisecond, 2 milliseconds, 3 milliseconds, 10milliseconds, etc.). The predetermined time period may be a reactiontime associated with the host vehicle. For example, the predeterminedtime period may be a delay between the time when a sensor (e.g., animaging device) of the host vehicle senses a condition that requires abraking response from the host vehicle (e.g., a target vehicle cominginto the path of the host vehicle) and the time when the host vehiclebegins braking at its maximum braking capability. In this example, itmay be assumed that, in a worst-case scenario, the host vehicleaccelerates at its maximum braking capability for the entirety of thedelay period. In some embodiments, the time period associated with thereaction time may be determined or approximated by the processingdevice. For example, the processing device may monitor the time betweenreceiving an image and determining that a braking response is needed. Asanother example, the processing device may determine a mean, median, ormode reaction time associated with a plurality of navigational responsesand use the mean, median, or mode reaction time when calculating acurrent stopping distance. For example, after tens, hundreds, orthousands of navigational responses, the processing device may determinethat the average time between a sensed event and a navigational responseis a particular value (e.g., any real number of milliseconds) and usethat value as the reaction time associated with the host vehicle.

Consistent with this disclosure, a determined current stopping distancemay include a minimum distance between the host vehicle and anotherobject (e.g., a target vehicle or VRU) after coming to a complete stop.The determined or predetermined minimum distance may correspond with apredetermined separation distance to be maintained between the hostvehicle and other vehicles. For example, the processing device may beprogrammed to include a determined or predetermined minimum distance ina calculation of a stopping distance. For example, a predeterminedseparation distance may be at least 1 m. In this example, the determinedor predetermined minimum distance may be d_(min) as discussed above.

Process 4800 may include a step 4812 for determining a current speed ofthe target vehicle and to assume a maximum braking capability of thetarget vehicle. Consistent with this disclosure, the at least oneprocessing device may be programmed to determine a current speed of atarget vehicle. In some embodiments, the speed of the target vehicle maybe determined based on the speed of the host vehicle. For example, oneor more sensors on a host vehicle may provide information related to thespeed of the host vehicle and an indication of the acceleration orchange in direction of a target vehicle in relation to the host vehicle.In some embodiments, the target vehicle speed may be determined based onanalysis of at least one image. The at least one image may be, forexample, the same image received by the processing device at step 4802that was used to identify the target vehicle at step 4806. In someembodiments, a plurality of images may be analyzed to determine a speedof the target vehicle. For example, a first image may depict the targetvehicle a first distance from the host vehicle and a second image maydepict the target vehicle a second distance from the host vehicle, theprocessing device may use the change in distance and the time betweenthe first and second images to determine a speed associated with thetarget vehicle. In some embodiments, the target vehicle speed may bedetermined based on analysis of an output from at least one of a LIDARsystem or a RADAR system associated with the host vehicle. For example,the processing device may use the speed of the host vehicle and adistance between the host vehicle and the target vehicle (as sensed by,for example, a LIDAR system) to determine a speed of the host vehicle.

In some embodiments, to account for a worst-case scenario, theprocessing device may be programmed to assume that the current speed ofthe target vehicle is less than or more than a sensed speed of thetarget vehicle. For example, if the target vehicle is traveling in frontof the host vehicle, the processing device may be programmed to reduce asensed speed using a predetermined value, a percentage, a formula, orthe like. For example, if the processing device determined, based oninformation from one or more sensors, that a target vehicle is travelingat 100 km/hr, it may adjust the sensed speed by 10% to assume that thevehicle is traveling at 90 km/hr. The speed of a target vehicle may becorrelated with the braking capacity of the target vehicle so assuming areduced speed of the target vehicle is akin to assuming the targetvehicle may stop quicker than it otherwise might (e.g., a target vehiclemay stop in a shorter distance if traveling at 90 km/hr than iftraveling at 100 km/hr).

Consistent with this disclosure, the at least one processing device maybe programmed to assume a maximum braking capability of the targetvehicle based on at least one recognized characteristic of the targetvehicle. The maximum braking capability may be assumed as part of step4812 of process 4800. The processing device may be programmed torecognize the at least one characteristic from information from one ormore sensors (e.g., LIDAR, RADAR, imaging devices, etc.). In someembodiments, the recognized characteristic of the target vehicle may bedetermined based on analysis of the at least one image. For example, theimage of the target vehicle may include a text on the exterior of thetarget vehicle, which may be used to determine a vehicle type, vehiclemodel, vehicle size, or other characteristic. As another example, theimage of the target vehicle may include other Objects that may be usedto approximate a vehicle size or other characteristic based oncomparison with the other objects. As a particular example, a largevehicle may appear taller than a speed-limit sign whereas a smallvehicle may appear shorter than a speed-limit sign. In some embodiments,the at least one characteristic of the target vehicle may be determinedbased on at least one of a LIDAR output or a RADAR output. For example,a LIDAR output may include a first distance associated with the distanceto the rear bumper of the target vehicle and a second distanceassociated with a distance to the front bumper (or other area) of thetarget vehicle, the difference between which may be used to estimate thesize of the target vehicle.

The at least one characteristic may be any characteristic that is knownto correlate with a braking capability or that may correlate with abraking capability. In some embodiments, the recognized characteristicof the target vehicle may include a vehicle type. The vehicle type maybe, for example, a general category to which the target vehicle belongs(e.g., full-size sedan, compact car, SUV, cross-over SUV, motorcycle,etc.) or a more particular category or sub-category associated with thetarget vehicle. The processing device may be programmed to assume thatthe target vehicle has a maximum braking capability corresponding withthat of a known braking capability of that vehicle type or a class ofvehicles. For example, if the target vehicle is determined to be afull-sized sedan, the processing device may assume that the targetvehicle has a maximum braking capability matching that of a full-sizedsedan having a best maximum braking capability (e.g., the full-sizedsedan that can come to a stop in the shortest distance compared to otherfull-sized sedans). In some embodiments, the recognized characteristicof the target vehicle may include a vehicle model, brand name, or otherclassifier of the target vehicle (e.g., Toyota Prius®, BMW X5®, etc.).The processing device may use the vehicle type to, for example, access adatabase containing known braking capabilities of each vehicle type. Forexample, if the detected vehicle type is BMW X5®, the processing devicemay look up the reported braking capabilities of a BMW X5® from adatabase. If there are multiple maximum braking capabilities reportedfor a vehicle model (for example, a BMW X5® may have different brakingcapabilities depending on whether it has the xDrive40i or xDrive50i trimlevel or depending on the year of its manufacture), the processingdevice may be programmed to assume the target vehicle has the bestmaximum braking capability reported for that vehicle model. In someembodiments, the recognized characteristic of the target vehicle mayinclude a vehicle size. The vehicle size may be a relative size, apredetermined size, or the like. The vehicle size may correspond to aphysical size of the vehicle and/or an estimated weight of the vehicle.For example, the processing device may determine that the target vehicleis larger or smaller than the host vehicle. In another example, theprocessing device may be programmed to classify the target vehicle intoone or a plurality of predetermined vehicle sizes, each of which mayinclude a range of sizes (e.g., category 1=less than 1,000 kg; category2=1,000-1500 kg; category 3=1,500-1,800 kg; and so forth). Some vehiclesmay contain an indication of its size, which may be used to determine avehicle size of the target vehicle. For example, the target vehicle maybe a GMC Sierra® and may include an indication on the exterior of thevehicle associated with its size, such as 1500, 2500, 2500HD, and soforth.

The current speed of the target vehicle and the assumed maximum brakingcapability of the target vehicle may be used to determine a targetvehicle travel distance comprising a distance it would take for thetarget vehicle to come to a complete stop from its current speed bybraking at its maximum braking capability. The distance may bedetermined by any means consistent with this disclosure.

Process 4800 may include a step 4814 for implementing the plannednavigational action if the planned navigation action is safe. For thepurposes of step 4814, one example of when the planned navigation actionmay be considered safe is when the determined current stopping distancefor the host vehicle is less than the determined next-state distancesummed together with a target vehicle travel distance. In someembodiments, the at least one processing device may be programmed toimplement the planned navigational action if the determined currentstopping distance for the host vehicle is less than the determinednext-state distance summed together with a target vehicle traveldistance. The target vehicle travel distance may be determined by anymeans consistent with this disclosure. For example, the target vehicletravel distance may be based on the current speed of the target vehicleand the assumed maximum braking capability of the target vehicle. Thistarget vehicle travel distance may correspond with a total distance thetarget vehicle will travel before coming to a complete stop. Thenavigational action may be implemented in this circumstance becausethere will be no collision between the host vehicle and the targetvehicle because the host vehicle's current stopping distance (includingthe potential distance traveled assuming maximum acceleration during thereactionary period) will allow it to come to a complete stop beforehitting the target vehicle even if the target vehicle brakes at itsmaximum braking capability. The processing device will implement thenavigational action because the host vehicle will be at least the RSSsafe distance from the target vehicle after performance of thenavigational action. In other words, the next-state distance is equal toor larger than the RSS safe distance. Conversely, if the next-statedistance is less than the RSS safe distance (e.g., the current stoppingdistance for the host vehicle is not less than the determined next-statedistance summed with the target vehicle travel distance) then theprocessing device may be programmed to deny or abort the navigationalaction, or to implement a different navigational action.

For the purposes of step 4814, one example of when the plannednavigation action may be considered safe is when the determined currentstopping distance for the host vehicle is less, by at least apredetermined minimum distance, than the determined next-state distancesummed together with the target vehicle travel distance, where thetarget vehicle travel distance is determined based on the current speedof the target vehicle and the assumed maximum braking capability of thetarget vehicle. In some embodiments, the at least one processing devicemay be configured to implement the planned navigational action if thedetermined current stopping distance for the host vehicle is less, by atleast a predetermined minimum distance, than the determined next-statedistance summed together with the target vehicle travel distance, wherethe target vehicle travel distance is determined based on the currentspeed of the target vehicle and the assumed maximum braking capabilityof the target vehicle. In this embodiment, the predetermined minimumdistance may be d_(min) and may be predetermined, or determined, by anymeans consistent with this disclosure and have any attribute discussedabove. In some embodiments, the predetermined minimum distance maycorrespond to a predetermined separation distance to be maintainedbetween the host vehicle and other vehicles. For example, a constraintof an autonomous navigation system may dictate that the autonomousvehicle never come within (less than) a specified distance of othervehicles. The predetermined separation distance may be a distance of anydimension. In some embodiments, the predetermined separation distance isat least 1 m, 2 m, 5 m, etc. In some embodiments, the predetermineddistance may vary depending upon, for example, the speed at which thehost vehicle is traveling, the location of the host vehicle (e.g., anurban road, a rural highway, etc.).

Consistent with this disclosure, the RSS model may be used to navigate afully autonomous vehicle, may be used to navigate a partially autonomousvehicle (e.g., a vehicle with a human-operable mode and a selectivelyautonomous mode), or may be used as an underlying safety feature in ahuman operable vehicle (e.g., a safety system may prevent or inhibithuman inputs in a human-operable vehicle that may be unsafe under theRSS model).

Comfort Responsibility-Sensitive Safety (CRSS)

RSS is effective for determining a safe distance between a host vehicleand another object (e.g., one or more target vehicles or VRUs). Some ofthe underlying calculations in RSS may assume a worst-case scenario andcall for the host vehicle to respond at its maximum capability. Forexample, some embodiments of RSS may define a safe area in which therewill not be a collision if both the target vehicle and the host vehiclebrake at their maximum braking capacity, and the host vehicle beginsbraking after a reaction time during which it accelerates at its maximumcapability.

While RSS may prevent or avoid accidents, some users of autonomousvehicles may find that the reactions required by RSS may not create themost comfortable or relaxing ride in certain circumstances. For example,if the worst-case scenario does arise, a vehicle operating in an RSSmode may brake at its maximum braking capability in at least somescenarios. In addition, RSS may define a safe distance between a hostvehicle and another object. If a target vehicle, VRU, or other object isfurther from a vehicle than the safe distance, the vehicle need not makeany navigational response. However, as the object comes within adistance equal to or less than the RSS safe distance, the vehicle mayrespond by braking at the maximum braking capability until the vehiclecomes to a stop or until an RSS distance has been established betweenthe object or the target vehicle. Such operation may subject thepassengers of the host vehicle to uncomfortable acceleration rates(e.g., during periods of time when the host vehicle brakes are appliedat maximum level), Accordingly, there may be a need for an autonomousvehicle safety model that allows for a more comfortable passengerexperience.

To provide for a more comfortable, human-like driving experience, anautonomous vehicle may be equipped with a navigation system configuredto operate using non-maximal navigational responses. For example, if anautonomous vehicle needs to slow down or stop to avoid a collision, thenavigation system may allow braking at a force that is less than themaximum braking capability of the vehicle, at least during a part of thebreaking period. Similarly, if a vehicle needs to turn, veer, or swerveto avoid a collision, the navigation system may allow a turn that isless than the maximum turning capability of the vehicle. The same may betrue for an acceleration response, which may carried out at less thanthe maximum acceleration capability of the vehicle, at least during apart of the acceleration period. By limiting the amount of braking oracceleration, a braking response by a host vehicle may be less abrupt,smoother, and feel more similar to a scheduled brake rather than anemergency or late brake. For example, a scheduled brake may include agradual decrease of the speed that does not cause a seatbelt to lockup.In another example, a scheduled brake may include a gradual increase ofthe breaking power, possibly until reaching the maximum breaking powerof the vehicle, by which point breaking may resume with maximum breakingpower.

Consistent with disclosed embodiments, a comfortresponsibility-sensitive safety (CRSS) safe distance may be determined.The CRSS safe distance may be the distance between a host vehicle andanother object (e.g., a target vehicle or VRU) at which the host vehiclemay comfortably come to a stop without colliding with the object.Consistent with this disclosure, CRSS may assume a gradual applicationof the brake from an initial braking force (that is less than themaximum braking capability of the vehicle) to the maximum brakingcapability of the vehicle rather than an immediate application of themaximum braking capability. At least in the context of CRSS, the termminimum breaking capability is sometime used interchangeably with theterm initial breaking force. The initial braking force may be a minimumbraking force of the vehicle or a fraction of the maximum brakingcapability of the vehicle. The CRSS safe distance may be determinedbased on a momentary calculated velocity of the host vehicle, themomentary velocity of the target vehicle, the comfort or sub-maximalbraking acceleration, and the response time.

Definition 28 (CRSS safe distance) A longitudinal distance between a carc_(r) and another car c_(f) that is in c_(r)'s frontal corridor is safew.r.t, a response time p if for any braking of at most a_(max,brake),performed by c_(f), if, c_(r) will apply a jerk-bounded braking andacceleration then it won't collide with c_(f):

In some embodiments, a comfortable navigation response may beaccomplished by decreasing the speed or velocity of a host vehicle by arestrained braking profile, Which may significantly reduce the jerk on avehicle and/or passenger thereof. Lemma 12 below calculates the CRSSsafe distance according to one embodiment wherein the brake of thevehicle is subject to a gradual braking profile rather than an immediateapplication of the maximum braking capability.

Lemma 12 Let c_(r) be a host vehicle which is behind a target vehiclec_(f) on the longitudinal axis. Let a_(max,brake) be the maximal brakingcapacity. Let v_(o) be the initial velocity of the host vehicle andv_(f) be the original velocity of the target vehicle. Let j_(max) be theslope of a linear application of the host vehicle's brake and let T bethe time for reaching MI brake in the host vehicle. Then, the CRSS safedistance for the host vehicle is:

$\lbrack {\lbrack {{v_{0}T} + {\frac{1}{2}a_{0}T^{2}} - {\frac{1}{6}j_{\max}T^{3}}} \rbrack + \frac{( {v_{0} + {a_{0}T} - {\frac{1}{2}j_{\max}T^{2}}} )^{2}}{2{❘a_{\min,{brake}}❘}} - \frac{v_{f}^{2}}{2{❘a_{\max,{brake}}❘}}} \rbrack{{CRSS}_{Distance} =}$

Proof CRSS assumes a jerk-bounded braking capability of the host vehiclethat is associated with decreasing the acceleration of the host vehiclelinearly (with slope j_(max)), until reaching a maximum brakingcapability a_(max,brake) and then continuing to brake with a constantdeceleration (correlated with a_(max,brake)) until reaching coming to astop. A vehicle braking with a jerk of j_(max) that has an initialacceleration a₀≤0 m/s, an initial velocity v_(o)≤0 m/s² and an initialposition x_(o)≤0 m has the following dynamics:a(t)=a ₀ −j _(max) tv(t)=v ₀+∫_(τ=0) ^(t) a(τ)dτ=v ₀ +[a ₀τ−½j _(max)τ²]₀ ^(t) =v ₀ +a _(v)t−½j _(max) t ²x(t)=x ₀+∫_(T=0) ^(t) v(τ)dτ=x ₀ +[v ₀τ−½a ₀τ²−⅙j _(max)τ²]₀ ^(t) =x ₀+v _(x) t+½a ₀ t ²−⅙j _(max) t ²

Based on these equations, the braking distance can be defined. Leta_(min,brake) be the minimum braking capability of the host vehicle andlet T be the first time in which either a(T)=a_(min,brake) or v(T)=0,that is,

${T = {\min\{ {T_{1},T_{2}} \}{where}}}{{T_{1} = \frac{a_{0} + a_{\min,{brake}}}{j_{\max}}},{T_{2} = \frac{a_{0} + \sqrt{a_{0}^{2} + {2j_{\max}v_{0}}}}{j_{\max}}}}$

The time for reaching the maximum brake capability by applying the brakelinearly with j_(max) is:

$T_{b} = \{ \begin{matrix}T_{2} & {{{if}T} = T_{2}} \\\frac{v_{0} + {a_{0}T} - {\frac{1}{2}j_{\max}T^{2}}}{a_{\min,{brake}}} & {otherwise}\end{matrix} $

The speed (velocity) of the host vehicle at any given time may also bedetermined as a function of j_(max) as follows:

${v(t)} = \{ \begin{matrix}{v_{0} + {a_{0}t} - {\frac{1}{2}j_{\max}t^{2}}} & {{{if}t} \leq T} \\{v_{0} + {a_{0}T} - {\frac{1}{2}j_{\max}T^{2}} - {( {t - T} )a_{\min,{brake}}}} & {{{if}t} \in ( {T,T_{b}} )} \\0 & {otherwise}\end{matrix} $

With the formulas for the time for reaching the maximum braking capacityand the speed of the host vehicle both during the period in which thebrake is being applied according to j_(max) and during the period inWhich the maximum brake a_(max,brake) is being applied (because thebrake was gradually applied using j_(max) until the maximum brakingcapability was reached), we can determined a braking distance for thehost vehicle:

$\lbrack {{v_{0}T} + {\frac{1}{2}a_{0}T^{2}} - {\frac{1}{6}j_{\max}T^{2}}} \rbrack + \frac{( {v_{0} + {a_{0}T} - {\frac{1}{2}j_{\max}T^{2}}} )^{2}}{2a_{\min,{brake}}}$

Consistent with this disclosure, the sub-maximal braking rate j_(max)may be predetermined or determined by a processing device. In someembodiments, j_(max) may be an ideal or statistically acceptable brakingrate. For example, data relating to the braking rate at which mosthumans come to a stop may be used for j_(max). In some embodiments,j_(max) may be set according to a user preference. For example, a firstpassenger may provide a first j_(max) that is comfortable to him or her,a second passenger may provide a second j_(max) that is comfortable tohim or her, and so forth. In some embodiments, a processing device maydetermine a j_(max) based on, for example, one or more roadcharacteristics, traffic conditions (congestion level, average distancebetween vehicle around the host vehicle, rate of cut-ins in front of thehost vehicle, etc.), one or more vehicle characteristics, one or moreweather characteristics, or the like. For example, a processing devicemay determine a j_(max) that provides the maximum safety and comfort ona snowy road, a second j_(max) that provides the maximum safety andcomfort on a dry highway, and so forth. It will be appreciated, thatwhile implementing j_(max) can help increase comfort and have otherpositive impacts on the behavior of the host vehicle, it can also haveless desirable effects, in particular, if j_(max) is small, so thatbreaking may become “relaxed.” or not as strong. For example, using asmall j_(max) can have a strong negative effect on efficiency, bycausing the vehicle to always keep an exaggerated distance from thevehicle ahead. This may cause an annoyance to other road users andprevent the host vehicle from effectively negotiating complex scenariossuch as merging and driving in congested areas. Thus, in some examples,a j_(max) that balances performance or efficiency with comfort (whilemaintaining RSS safety) can be set, selected or determined.

Consistent with this disclosure, the sub-maximal braking rate j_(max)may be a constant. For example, the sub-maximal braking rate may be abraking rate that corresponds with a deceleration of 2 m/s², 10 m/s², orany other constant deceleration. In some embodiments, the sub-maximalbraking rate may be constant that is proportional to the maximum brakingrate capability of a host vehicle. For example, the sub-maximal brakingrate may be 20%, 33%, 50%, 70%, or any other percentage of the maximumbraking capability of the host vehicle. In some embodiments, thesub-maximal braking rate may be a linear function of the current speedof the host vehicle, such that the brake is gradually applied from theminimum braking capability of the host vehicle up to, at most, themaximum braking capability of the host vehicle. For example, asub-maximal braking rate may be determined that allows the host vehicleto come to a stop from its current speed without reaching the maximumbraking capability of the vehicle. As another example, a sub-maximalbraking rater may be determined that eventually reaches the maximumbraking capability of the host vehicle such that the host vehicle brakesat less than maximum braking capability for a first portion of astopping maneuver and brakes at its maximum braking capability for asecond portion the stopping maneuver. In some embodiments, thesub-maximal braking rate may be a different function of the currentspeed of the vehicle. For example, the sub-maximal braking rate may be abraking rate that is exponentially or logarithmically applied until thevehicle comes to a stop.

Consistent with this disclosure, the CRSS safe distance may be used inany embodiment discussed above in relation to RSS. In practice, CRSSrequires an autonomous vehicle to begin braking sooner than a vehicleoperating in an RSS mode. With CRSS, the vehicle applies the brake atmost at the rate dictated by j_(max) where as in RSS, the vehicle maybrake at its maximum braking capability. As such, a CRSS safe distancemay be longer than an RSS safe distance.

Consistent with this disclosure, a CRSS model may the RSS assumptionthat the host vehicle may accelerate at its maximum accelerationcapability for an initial response period before braking at the rateassociated with j_(max) until coming to a stop. As another example, CRSSmay include the RSS assumption that the host vehicle stop leaving aminimum approach distance from a target vehicle after applying the brakeat a rate associated with j Max until coming to a stop.

In some embodiments, CRSS may be modified such that a vehicle may brakeat a sub-maximal braking period during a first period and may brake atits maximum braking capability during a second period. For example, ahost vehicle traveling behind a target vehicle may sense that the targetvehicle is coming to a stop and the host vehicle may then brake at asub-maximal braking capability (e.g., gradually brake at j_(max)) for afirst duration (or until a first distance is traveled) and brake at amaximum braking capability for a second duration (or until a seconddistance is traveled). In this example, the CRSS safe distance may beshorter than if the vehicle were programmed to only brake at thesub-maximal braking capability for the entire period. In someembodiments, CRSS may be modified such that the host vehicle may brakeat a first sub-maximal braking capability for a first period and asecond sub-maximal braking capability for a second time period. Forexample, the host vehicle may be programmed to brake at a first rate(e.g., a first j_(max)) for a first duration or distance and to brake ata second rate (e.g., a second j_(max)) for a second duration ordistance. In this example, the first rate may be less than the secondrate. Such a mode of operation may enable a host vehicle to re-establisha CRSS distance, for example, without braking at a rate higher that alevel associated with j_(max).

In some embodiments, a passenger or user of a host vehicle may selectone or more navigation modes that determine the sub-maximal brakingrate. For example, the passenger may be able to select whether the hostvehicle brakes with a braking profile associated with a constantsub-maximal braking rate, a gradually increasing sub-maximal brakingrate, an exponentially increasing sub-maximal braking rate. Any otherbraking rate profile may be employed. For example, a selectable mode mayinstruct the host vehicle to constantly apply the predeterminedsub-maximal braking rate until the host vehicle is stopped or until abraking condition is determined to no longer exist. As another example,a selectable mode may instruct the host vehicle to constantly apply thepredetermined sub-maximal braking rate for at least a portion of a timeperiod during which a braking condition is determined to exist followedby an application of the host vehicle brake at its maximum braking ratecapability. As another example, a selectable mode may instruct the hostvehicle to apply the brake beginning at the predetermined sub-maximalbraking rate and to progressively increase the braking rate up to themaximum braking rate capability of the host vehicle. Any othercombination of braking rates may be selected.

Consistent with this disclosure, CRSS may be used in association with anRSS modem or may be used instead of an RSS mode. In some embodiments,CRSS may be selectively used in some circumstances while RSS may be usedin other circumstances. For example, CRSS may be used on a highway(e.g., where the host vehicle is traveling at a high rate of speed andbraking at a maximum braking capability may be highly uncomfortable) andRSS may be used in an urban setting (e.g., where the host vehicle istraveling at a low speed and making frequent stops at traffic lights,stop signs, etc.). In some embodiments, a host vehicle may be able toautomatically switch between CRSS and RSS modes. For example, the systemmay switch to CRSS upon sensing the host vehicle has entered a highwayenvironment, may switch to RSS upon sensing an urban environment, and/ormay switch to CRSS in certain sensed weather conditions (e.g., snow,rain, etc.).

In some embodiments, CRSS may be used to ensure that a host vehicleremains at least a CRSS safe distance from a target vehicle (or VRU orother object) at all times. For example, if a target vehicle changeslanes and is ahead of the host vehicle after the lane change by adistance less than the CRSS distance, the host vehicle may brake at asub-maximal braking rate (e.g., a j_(max) braking rate) until it is adistance from the target vehicle that is equal to or greater than theCRSS safe distance. In this example, if the target vehicle comes to acomplete stop, the host vehicle may brake at the sub-maximal brakingrate until coming to a complete stop or may apply a braking profile thatbegins at a sub-maximal rate and increases up to a maximum braking rate.Likewise, if the target vehicle brakes for a period but continuestraveling in front of the host vehicle, the host vehicle may brake atthe sub-maximal braking rate until the target vehicle is at least a CRSSsafe distance away from the target vehicle, then the host vehicle maycontinue traveling at its current speed or at a new speed that allowsthe host vehicle to maintain the CRSS distance. As noted above, the hostvehicle will not take an active navigational action relative to a targetvehicle if the CRSS distance, in this mode, cannot be maintained. Insome embodiments, the processing device may determine that the hostvehicle is approaching the CRSS safe distance (e.g., the host vehicle ismore than the CRSS safe distance from a target vehicle, but will be atthe CRSS safe distance if it continues at its current acceleration orcurrent speed) and may remove acceleration without braking to maintain adistance that is greater than the CRSS safe distance. For example, thehost vehicle may release the throttle, causing the host vehicle to coastaway from a target vehicle in front of the host vehicle when the hostvehicle would otherwise come within the CRSS safe distance if it did notcoast.

In some embodiments, RSS may be implemented as an emergency measure whenCRSS is used. For example, when a target vehicle cuts in front of a hostvehicle and the distance (through no fault of the host vehicle) to thetarget vehicle in front of the host vehicle is less than the CRSS safedistance, the host vehicle may brake according to the RSS mode (e.g.,immediately breaking at its maximum braking capability). In particular,RSS breaking may be used if the cut in creates a distance that is equalto or less than the RSS safe distance (which is shorter than the CRSSsafe distance). If the distance is greater than the RSS safe distancebut is less than a CRSS safe distance, than in one example, the systemmay determine a j_(max) that can be used to stop the host vehicle safelyaccording to the current distance (which is somewhere between CRSS safedistance and RSS safe distance) and adjust CRSS accordingly so that thevehicle stops using the determined j_(max) during at least a portion ofthe breaking period.

FIGS. 49A-49D illustrate the concept of a safe distance under the CRSSmodel when a host vehicle is traveling behind a target vehicle, FIG. 48Ashows a CRSS safe distance 4902 between a host vehicle 4904 and a targetvehicle 4906. As discussed above, CRSS safe distance 4902 is thedistance needed for host vehicle 4904 to come to a stop withoutcolliding with target vehicle 4906 if host vehicle 4904 brakes at acomfortable braking rate j_(max) that is less than its maximum brakingcapability. For comparison purposes, RSS safe distance 4702 (as shown inFIGS. 47A-47D) is included. RSS safe distance 4702 is the distanceneeded for host vehicle 4904 to come to a stop if it brakes at itsmaximum braking capability.

FIG. 4913 shows a CRSS safe distance 4912 between a host vehicle 4914and a target vehicle 4916. The difference between CRSS safe distance4902 and CRSS safe distance 4912 may be that CRSS safe distance 4912 isassociated with a lower braking rate than CRSS safe distance 4902. Thatis, the j_(max) associated with host vehicle 4814 is lower than thej_(max) associated with host vehicle 4904, therefore, host vehicle 4914will require a longer distance to come to a stop.

FIG. 49C illustrates CRSS safe distance 4922 between a host vehicle 4924and a target vehicle 4926. In this example, CRSS safe distance 4922include a minimum distance 4910, which may be a minimum separationbetween host vehicle 4924 and target vehicle 4926 after host vehiclecomes to a stop by braking with at a rate of j_(max) (as shown by CRSSsafe distance 4902). As discussed above, minimum distance 4910 may bed_(min).

FIG. 49D illustrates CRSS safe distance 4932 between a host vehicle 4934and a target vehicle 4936. In this example, CRSS safe distance 4932includes both minimum distance 4910 and acceleration distance 4908.Acceleration distance 4908 may be the distance that host vehicle 4934would travel if it accelerated at a maximum acceleration capabilityduring an initial reaction period.

The concept of the CRSS safe distance may be extended into lateraldirections. A person skilled in the art having the benefit of thisdisclosure would recognize that a CRSS safe distance may include alateral distance between a host vehicle and another object (e.g., atarget vehicle or VRU) within which the host vehicle may adjust thesteering of the host vehicle to avoid collision with the object whileavoiding an uncomfortable steering adjustment.

Consistent with this disclosure, a system for braking a host vehicle isdisclosed. The system may be, for example, braking system 230 or may beincluded in a navigational system, for example, an ADAS system. Thebraking system may include at least one processing device. Theprocessing device may be programmed to perform one or more methods,processes, operations, or functions consistent with this disclosure.

FIG. 50 is a flowchart depicting an exemplary process 5000 that may beperformed by the at least one processing device of the braking system.Process 5000 is used for explanatory purposes and is not intended to belimiting. One of ordinary skill in the art having the benefit of thisdisclosure may understand that process 5000 may include additionalsteps, may exclude certain steps, or may be otherwise modified in amanner consistent with this disclosure.

Process 5000 may include a step 5002 for receiving an outputrepresenting an environment of a host vehicle. Consistent with thisdisclosure, the at least one processing device may be programmed toreceive an output representative of an environment of the host vehicle.The output may be received, for example, from at least one sensorincluded in or in communication with the braking system. The at leastone sensor may be any sensor disclosed herein including, for example, animage capture device, a LIDAR system, a RADAR system, an accelerometer,or the like. In some embodiments, the processing device may beprogrammed to receive a plurality of outputs from one or more sensors.For example, the processing device may receive a first output from animage capture device, a second output from a LIDAR system, and so forth.As another example, the processing device may be programmed to receive afirst output from an image capture device, a second output from theimage capture device, and so forth. In some embodiments, the one or moresensors may be configured to capture information relating to differentareas of the environment of the host vehicle. For example, a first imagecapture device may be configured to capture an image of the environmentin front of the host vehicle, a second image capture device may beconfigured to capture an image of the environment behind the hostvehicle, and so forth. As another example, an image capture device maybe configured to capture an image of the environment in front of thehost vehicle and one or more LIDAR systems may be configured to captureinformation relating to the environment on either side of the hostvehicle.

Process 5000 may include a step 5004 for detecting a target vehicle inthe environment of the host vehicle. In some embodiments, the targetvehicle may be detected based on the output received at step 5002.Consistent with this disclosure, the at least one processing device ofthe braking system may be programmed to detect, based on the output, atarget vehicle in the environment of the host vehicle. The targetvehicle may be detected by any means consistent with this disclosure.For example, if the output is one or more images, the processing devicemay analyze the images (e.g., compare the images to images know tocontain vehicles) to detect a target vehicle. As another example, one ormore outputs from one or more LIDAR system or RADAR systems may be usedto detect the outline and position of a target vehicle. In someembodiments, the processing device may detect a plurality of targetvehicles. For example, the processing device may detect a target vehiclein front of the host vehicle, behind the host vehicle, and/or next tothe target vehicle, or a combination thereof. While the examplesdisclose detecting target vehicles, it is understood that any otherobject (e.g., VRUs, road characteristics, etc.) may be detected by thesame means.

Process 5000 may include a step 5006 for determining a speed of the hostvehicle and a distance between the host vehicle and the target vehicle.Consistent with this disclosure, the at least one processing device ofthe braking system may be programmed to determine a current speed of thehost vehicle and a current distance between the host vehicle and thetarget vehicle. The current speed and/or the current distance may bedetermined based on one or more outputs from one or more sensors. Insome embodiments, the current speed and/or the current distance may bedetermined based on the outputs used to detect the target vehicle atstep 5004. For example, an output from a LIDAR system may output one ormore distances between various points on the target vehicle and the hostvehicle, which may be used to determine a current distance between thehost vehicle and the target vehicle. In some embodiments, the currentspeed of the host vehicle may be provided by an accelerometer and/orspeedometer associated with the host vehicle.

Process 5000 may include a step 5008 for determining whether a brakingcondition exists, Consistent with this disclosure, the at least oneprocessing device of the braking system may determine whether a brakingcondition exists. A braking condition may be any condition in which thehost vehicle needs to brake to avoid unsafe circumstances, avoid acollision, or come to a stop. For example, a braking condition may be adetermination that the host vehicle is less than the CRSS safe distanceaway from the target vehicle or other object. The determination ofwhether a braking condition exists may be based at least upon thecurrent speed of the host vehicle and the current distance between thehost vehicle and the target vehicle. For example, the processing devicemay determine a CRSS safe distance (or RSS safe distance) between thetarget vehicle and the host vehicle based on the current speed of thehost vehicle and target vehicle, the braking capability of the hostvehicle, the assumed braking capabilities of the target vehicle, andoptionally, the maximum acceleration rate of the host vehicle, asdiscussed above. The processing device may the compare the CRSS safedistance with the current distance between the host vehicle and thetarget vehicle. The processing device may determine that a brakingcondition exists if, based on the comparison, the current distancebetween the host vehicle and the target vehicle is less than the CRSSsafe distance. Any other unsafe condition disclosed herein to which thehost vehicle would respond by braking may be a braking condition. Abraking condition would also exist if the host vehicle detects that at acurrent speed and/or acceleration, the host vehicle will approach atarget vehicle closer than the CRSS distance. In such cases, the hostvehicle would take action by braking, or instituting another maneuver(lane change etc.) such that the CRSS distance is at least maintainedbetween the host vehicle and the target vehicle.

Process 5000 may include a step 5010 for causing application of abraking device according to a predetermined braking profile if a brakingcondition exists. The braking condition may be any braking conditiondetermined at step 5008. Consistent with this disclosure, the at leastone processing device of the braking system may be programmed to, if abraking condition is determined to exist, cause application of a brakingdevice associated with the host vehicle according to a predeterminedbraking profile. For example, if the processing device determines thatthe host vehicle is less than or is approaching a CRSS safe distancerelative to a target vehicle, the braking system may begin braking thehost vehicle at a predetermined sub-maximal braking rate. Thepredetermined braking profile may include a segment beginning at asub-maximal braking rate for the host vehicle and may progressivelyincrease up to a maximum braking rate of the host vehicle. Thesub-maximal braking rate may progressively increase according to any ofthe embodiments disclosed herein. For example, the progressive increasemay be a non-linear increase. In another example, the progressiveincrease may be a linear increase.

For example, the braking system may only apply the brake during theduration of the braking condition. In some embodiments, once the maximumbraking rate of the host vehicle is achieved, the at least one processormay be configured to continue the application of the braking device ofthe host vehicle at the maximum braking rate of the host vehicle untilthe braking condition ceases to exist (e.g., the host vehicle stops or aCRSS distance is reestablished between the host vehicle and the targetvehicle). In some cases, the braking condition may cease before the hostvehicle comes to a complete stop, even when applying the brakingmechanism at the maximum braking rate, and the processing device maycease the braking in response to the end of the braking condition. Insome embodiments, the maximum braking rate of the host vehicle may notbe achieved. For example, if the braking condition ceases to existbefore the braking system reaches the maximum braking rate, the at leastone processor may be programmed to cease braking and the maximum brakingrate of the host vehicle may never be reached.

In some embodiments, the maximum braking capability that is used tocompute breaking distances may be a certain number (or any othermathematical expression) that is used in the formulae that are used anddescribed herein. In some embodiments, the maximum braking force mayvary with respect to that which was used in the formulae and may be theactual breaking force that the vehicle is capable of producing at eachand every instant, and Which may be effected by, for example, dynamicfactors including road surface characteristics, weather conditions, andconditions of the vehicle and its various systems and components.

Consistent with this disclosure, a system for navigating a host vehicleis disclosed. In some embodiments, the system may be an ADAS system orother navigational system disclosed herein. The navigation system mayinclude at least one processor or processing device programmed toperform one or more methods, process, functions, or operationsconsistent with this disclosure. The processor or processing device maybe processing device 110 or another processor or processing device in orin communication with a host vehicle (e.g., the at least one processingdevice of the braking system).

FIG. 51 is a flowchart depicting an exemplary process 5100 that may beperformed by the at least one processing device of the navigationalsystem. Process 5100 is for explanatory purposes and it not intended tobe limiting. One of ordinary skill in the art having the benefit of thisdisclosure may understand that process 5100 may include additionalsteps, exclude certain steps, or may be otherwise modified in a mannerconsistent with this disclosure.

Process 5100 may include a step 5102 for receiving at least one imagerepresenting an environment of a host vehicle. Consistent with thisdisclosure, the at least one processing device may be programmed toreceive at least one image representative of an environment of a hostvehicle. The at least one image may be received from an image capturedevice. The image capture device may be any consistent with thisdisclosure, including image capture device 122. In some embodiments, theat least one image may be an image obtained from any of a camera, aRADAR, a LIDAR, or any other device from which an image may be obtained,whether optical or otherwise.

Process 5100 may include a step 5104 for determining a plannednavigational action. Consistent with this disclosure, the at least oneprocessing device may be programmed to determine a planned navigationaction for accomplishing a navigational goal of the host vehicle. Thenavigation action may be determined based on at least one drivingpolicy. The planned navigation action and/or the at least one drivingpolicy may be any consistent with this disclosure, including thosediscussed above. For example, the planned navigation action may includeat least one of a lane change maneuver, a merge maneuver, a passingmaneuver, a follow distance reduction maneuver, or a maintain throttleaction. The navigational action may be determined in substantially thesame manner as discussed with respect to step 4804 of process 4800. Theprocessing device may be programmed to analyze the at least one image toidentify a target vehicle in the environment of the host vehicle. The atleast one image may be an image received from an image capture device,such as image capture device 122. The target vehicle may be a vehicleanywhere in the current vicinity of the host vehicle or a futurevicinity of the host vehicle. For example, the target vehicle may be avehicle in front of, next to, or behind the host vehicle and/or avehicle that will be in front of, next to, or behind the host vehicle ifit performs the planned navigation action.

Process 5100 may include a step 5106 for determining a next-statedistance associate with the planned navigational action. Consistent withthis disclosure, the at least one processing device may be programmed todetermine a next-state distance between the host vehicle and the targetvehicle that would result if the planned navigation action was taken.The next-state distance may be calculated by any means disclosed herein,including the CRSS safe distance formula above. For example, if theplanned navigation action is an acceleration (or a lane change, or evencontinuing at a current speed without application of a brake, etc.) ofthe host vehicle, the next-state distance may be a distance between thehost vehicle and a target vehicle in front of the host vehicle. In someexamples, more than one next-state distance may be determined. Forexample, if the planned navigation action is a merge into an adjacentlane, a first next-state distance may be determined in relation to thehost vehicle and a first target vehicle that will be in front of thehost vehicle after the merge and a second next-state distance may bedetermined in relation to a second target vehicle that will be behindthe host vehicle after the merge.

Process 5100 may include a step 5108 for determining a current speed ofthe host vehicle. Consistent with this disclosure, the at least oneprocessing device may be programmed to determine a current speed of thehost vehicle. The current speed may be determined by any meansconsistent with this disclosure, including as discussed in relation tostep 4808 of process 4800. In some embodiments, the current speed of thehost vehicle may be determined based on an output of one or moresensors. For example, the current speed may be determined from an outputof an accelerator, a LIDAR system, a RADAR system, a GI'S unit, or thelike. As another example, the current speed of the host vehicle may bedetermined by analyzing one or more images (e.g., based on a scalingrate change of a fixed object detected in two or more images).

Process 5100 may include a step 5110 for determining a current speed ofthe target vehicle and to assume a maximum braking capability of thetarget vehicle. Consistent with this disclosure, the at least oneprocessing device may be programmed to determine a current speed of thetarget vehicle and assume a maximum braking rate capability of thetarget vehicle. The maximum braking rate capability may be assumed basedon at least one characteristic of the target vehicle. The maximumbraking capability of the target vehicle may be determined by any meansconsistent with this disclosure, including those discussed in relationto RSS (e.g., as part of step 4812 of process 4800).

In some embodiments, the current speed of the target vehicle may bedetermined based on the current speed of the host vehicle. For example,one or more sensors of the host vehicle may provide information relatedto the speed of the host vehicle and one or more sensors may provide aposition of the target vehicle in relation to the host vehicle and/or achange in position, acceleration, or velocity of the target vehicle,which may be used to determine a current speed of the target vehicle. Insome embodiments, the target vehicle speed may be determined based onanalysis of at least one image. The at least one image may be the sameimage in which the target vehicle was first detected or may a differentimage. In some embodiments, a plurality of images may be analyzed todetermine a current speed of the target vehicle. For example, an imagecaptured at a first time may depict the target vehicle a first distancefrom the host vehicle and an image captured at a second time may depictthe target vehicle a second distance from the host vehicle, theprocessing device may determine a current speed based on the change indistance between the two images. In some embodiments, the target vehiclespeed may be determined based on analysis of an output from at least oneof a LIDAR system or a RADAR system associated with the host vehicle.For example, the processing device may use the speed of the host vehicleand a distance between the host vehicle and the target vehicle (assensed by, for example, a LIDAR system) to determine a speed of the hostvehicle.

The at least one characteristic of the target vehicle may be determinedby any means consistent with this disclosure. In some embodiments, theprocessing device may determine the at least one characteristic based onone or more outputs from one or more sensors associated with the hostvehicle. For example, the at least one characteristic may be determinedbased on at least one of a LIDAR output or a RADAR output. For example,a LIDAR output may include one or more distances associated with thedistance between, for example, the host vehicle and the top edge of thetarget vehicle and a bottom edge of the target vehicle, the differencebetween which may be used to determine a size of the target vehicle. Insome embodiments, the at least one characteristic may be determinedbased on analysis of at least one image. The at least one image may bethe image in which the target vehicle was first detected or a differentimage. For example, the image of the target vehicle may include text,logos, or other information that may be used to determine a vehicletype, model, trim level, or other characteristics another example, theimage of the target vehicle may include other vehicles or objects thatmay be used for comparison with the target vehicle to determine a sizeof the target vehicle.

The recognized characteristic of the target vehicle may be any that maybe useful for determining a maximum braking capability of the targetvehicle. In some embodiments, the recognized characteristic of thetarget vehicle may include a vehicle type. The vehicle type may be, forexample, a general category to which the target vehicle belongs (e.g.,full-size sedan, compact car, SUV, cross-over SUV, motorcycle, etc.) ora more particular category or sub-category associated with the targetvehicle. The processing device may be programmed to assume that thetarget vehicle has a maximum braking capability corresponding with thatof a known braking capability of that vehicle type or a class ofvehicles. For example, if the target vehicle is determined to be amotorcycle, the processing device may assume that the target vehicle hasa maximum braking capability matching that of the motorcycle having thebest maximum braking capability (e.g., the motorcycle that can come to astop the quickest or in the shortest difference). In some embodiments,the recognized characteristic of the target vehicle may include avehicle model. The vehicle model may include, for example, a brand nameand/or model name of the vehicle. The vehicle model of the targetvehicle may be determined by any means consistent with this disclosureincluding, for example, detection of text, logos, or other identifiersof a vehicle model or detection of features characteristic of a vehiclemodel. For example, the processing device may analyze an image of thetarget vehicle and recognize text associated with a vehicle model (e.g.,the text “Honda Accord” may be detected on the rear of the targetvehicle). As another example, the processing device may analyze an imageand recognize one or more distinctive features of the target vehicle(e.g., the shape of the taillights, the presence or absence of aspoiler, the general shape of the target vehicle, etc.) and maydetermine a vehicle type by, for example, comparing the recognizedfeatures with one or more images of known vehicle types. The processingdevice may use the vehicle type to determine the braking capabilities ofthe target vehicle. For example, if the vehicle type is Ford Escapee,the processing device may access a database or perform an Internetsearch to locate the reported braking capabilities of a Ford Escapee.Some vehicle types may have multiple reported braking capabilitiesdepending upon, for example, the features offered in the trim level ofthe vehicle. The processing device may be programmed to assume that thetarget vehicle has the best maximum braking capability of the vehiclesof that type. In some embodiments, the recognized characteristics of thetarget vehicle may include a vehicle size. The vehicle size may be aphysical dimension of the vehicle, a weight associated with the vehicle,a combination thereof, or the like. The vehicle size may be a relativesize, one of a plurality of predetermined sizes, or the like. Forexample, the processing device may be programmed to categorize targetvehicles into one of a plurality of predetermined size ranges (e.g.,compact=less than 1,000 kg; small=1,000-1,500 kg; and so forth). In someembodiments, the target vehicle size may be estimated based on itscomparison to the size of the host vehicle, to other vehicles on theroad, to objects near the target vehicle, and so forth. For example, theprocessing device may analyze an image of the target vehicle anddetermine that it is larger than the host vehicle but smaller than avehicle next to the target vehicle. The vehicle size may be used toassume a maximum braking capability of the target vehicle. For example,the processing device may be programmed to assume that larger, heaviervehicles take longer to come to a stop.

The maximum braking capability of the target vehicle may be determinedbased on additional factors. For example, the current maximum brakingcapability of the target vehicle may be determined based on a sensedcondition of a road surface. In this example, the sensed road conditionmay include a roughness of the road, a slant or slope of the road, thepresent or absence of a substance or an object on the road, whether theroad is asphalt, cement, gravel, or another material, or any othercondition consistent with this disclosure. As another example, thecurrent maximum braking capability of the target vehicle may bedetermined based on a sensed weather condition. In this example, theweather condition may include a detection of any precipitation (e.g.,rain, sleet, snow, ice, etc.), a weather condition that affectsvisibility (e.g., fog, smog, smoke, etc.), a weather condition that mayaffect the handling of the vehicle (e.g., strong winds, high heat,etc.), or any other weather condition that may affect a navigationalresponse of the host vehicle. In another example, processing device maydetermine a maximum braking capability based on whether the host vehiclecontains, for example, new or old tires, 1 passenger or a plurality ofpassengers, a significant weight of cargo, a trailer, etc. In someembodiments, the maximum braking capability of the target vehicle may bedetermined based on a predefined factor, such as a regulation whichprovides a maximum braking capability allowed for vehicles or vehicletypes.

The assumed maximum braking capability may be used to determine a targetvehicle travel distance that it may take the target vehicle to come to astop from its current speed if it were to brake at its maximum brakingcapability. The distance may be calculated by any means consistent withthis disclosure, including those discussed in relation to RSS and/orCRSS.

Process 5100 may include a step 5112 for implementing the navigationalaction if the planned navigational action is safe. For the purposed ofstep 5112, one example of when the planned navigation action may beconsidered safe is when the host vehicle can be stopped using asub-maximal braking rate within a host vehicle stopping distance that isless than the determined next-state distance summed together with atarget vehicle travel stopping distance determined based on the currentspeed of the target vehicle and the assumed maximum braking ratecapability of the target vehicle. In some embodiments, the at least oneprocessing device may be programmed to implement the plannednavigational action if, for the determined current speed of the hostvehicle and at a predetermined sub-maximal braking rate, the hostvehicle can be stopped within a host vehicle stopping distance that isless than the determined next-state distance summed together with atarget vehicle travel distance. The predetermined sub-maximal brakingrate may be less than a maximum braking rate capability of the hostvehicle. The target vehicle travel distance may be a distance determinedbased on the current speed of the target vehicle and the assumed maximumbraking rate capability of the target vehicle. As described above, thesub-maximal braking rate may be the jerk-bounded braking raterepresented by j_(max) in the CRSS formulas. In some embodiments, thesub-maximal braking rate may be any deceleration rate associated with,but less than, the maximum braking capability of the host vehicle. Forexample, the predetermined sub-maximal braking rate may be associatedwith a deceleration rate that is up to 50% of a deceleration rateassociated with the maximum braking rate capability for the hostvehicle. In another example, the predetermined sub-maximal braking ratemay be associated with a deceleration rate that is up to 20% of adeceleration rate associated with the maximum braking rate capabilityfor the host vehicle. In some embodiments, the maximum braking ratecapability of the host vehicle may be determined such that thesub-maximal braking rate can be determined. The maximum braking ratecapability may be determined based on any means consistent with thisdisclosure, including those discussed in relation to RSS. For example,the maximum braking rate capability of the host vehicle may bedetermined based on a sensed condition of a road surface. As anotherexample, the maximum braking rate capability of the host vehicle may bedetermined based on a sensed weather condition.

In some embodiments, as discussed above, the predetermined sub-maximalbraking rate may be a sub-maximal braking rate selected by a user. Forexample, the predetermined sub-maximal braking rate may be determinedbased on a user-selectable braking mode including: a mode in which ahost vehicle brake is constantly applied at the predeterminedsub-maximal braking rate until the host vehicle is stopped or a brakingcondition is determined to no longer exist; a mode in which a hostvehicle brake is constantly applied at the predetermined sub-maximalbraking rate fir at least a portion of a time period during which abraking condition is determined to exist followed by an application ofthe host vehicle brake at a maximum braking rate for the host vehicle;and/or a mode in which a host vehicle brake is applied beginning at thepredetermined sub-maximal braking rate and progressively increasing upto a maximum braking rate for the host vehicle.

Consistent with this disclosure, the host vehicle stopping distance maybe determined using one or more of the CRSS formulas discussed above.For example, the host vehicle stopping distance may be determined basedon the current speed of the host vehicle and the predeterminedsub-maximal braking rate of the host vehicle. As another example, thehost vehicle stopping distance may be determined based on the currentspeed of the host vehicle, the maximum acceleration that the hostvehicle could achieve during a response period, and the predeterminedsub-maximal braking rate of the host vehicle. In some embodiments, thehost vehicle stopping distance may be greater than a sum of anacceleration distance, which corresponds to a distance the host vehiclecan travel at a maximum acceleration capability of the host vehicle overa predetermined time period, and a maximum brake rate distance, whichcorresponds to a distance the host vehicle may travel while slowing fromthe current speed of the host vehicle to zero speed at a maximum brakingrate capability of the host vehicle. In some embodiments, the hostvehicle stopping distance may be greater than a sum of an accelerationdistance, which corresponds to a distance the host vehicle can travel ata maximum acceleration capability of the host vehicle over apredetermined time period, and a sub-maximal brake rate distance, whichcorresponds to a distance the host vehicle may travel while slowing fromthe current speed of the host vehicle to zero speed at a predeterminedsub-maximal braking rate capability of the host vehicle. In anyembodiment, the predetermined time period may be a reaction timeassociated with the vehicle. For example, the predetermined time periodmay the time period between the processing device first detecting thetarget vehicle and the time that the host vehicle begins braking, asdiscussed above in relation to RSS.

In some embodiments, the host vehicle stopping distance may include afirst distance over which the host vehicle is braked at thepredetermined sub-maximal braking rate and a second distance over whichthe host vehicle is braked at the maximum braking rate capability of thehost vehicle. For example, as discussed above, the host vehicle maybrake at the sub-maximal braking rate according to CRSS for a firstdistance and then brake at the maximal braking rate for a seconddistance. In another example, the host vehicle may brake at thesub-maximal braking rate and gradually increase the sub-maximal brakingrate until reaching the maximum braking rate and then continue brakingat the maximum braking rate. The processing device may be configured tocause the host vehicle to brake at the predetermined sub-maximal brakingrate over the first distance prior to braking the host vehicle at themaximum braking rate capability of the host vehicle over the secondduration. For example, the host vehicle may brake at the sub-maximalbraking rate according to CRSS for a first duration and then brake atthe maximal braking rate for a second duration.

Another example of when the planned navigation action may be consideredsafe at step 5112 is when he host vehicle can be stopped using apredetermined sub-maximal braking rate within a host vehicle stoppingdistance that is less than the determined next-state distance summedtogether with a target vehicle travel distance determined based on thecurrent speed of the target vehicle and the assumed maximum braking ratecapability of the target vehicle, wherein the predetermined braking rateprofile progressively increases from a sub-maximal braking rate to amaximal braking rate for the host vehicle. In some embodiments, the atleast one processing device may be programmed to implement the plannednavigational action if, for the determined current speed of the hostvehicle and for a predetermined braking rate profile, the host vehiclecan be stopped within a host vehicle stopping distance that is less thanthe determined next-state distance summed together with a target vehicletravel distance determined based on the current speed of the targetvehicle and the assumed maximum braking rate capability of the targetvehicle, wherein the predetermined braking rate profile progressivelyincreases from a sub-maximal braking rate to a maximal braking rate forthe host vehicle. The target vehicle stopping distance may be determinedas discussed with respect to the above embodiments. The differencebetween this embodiment and the prior embodiment is that the brakingprofile in this embodiment may progressively increase up to the maximumbraking rate for the host vehicle. The CRSS safe distance may include adistance within which (at current speeds for the host and targetvehicles) the host vehicle can stop and not collide with the targetvehicle when the host vehicle applies its brakes at a sub-maximal ratefor at least some of the braking period, and the target vehicle brakesat its maximum rate.

In this embodiment, the braking rate profile may increase by any meansconsistent with this disclosure. For example, the predetermined brakingrate profile may increase linearly from the sub-maximal braking rate tothe maximal braking rate for the host vehicle. As another example, thepredetermined braking rate profile may increase non-linearly from thesub-maximal braking rate to the maximal braking rate for the hostvehicle. In this example, the predetermined braking rate profile mayincrease exponentially, logarithmically, or according to any otherfunction or may increase sporadically. In any example, it remainspossible that the braking profile never reaches the maximum brakingcapability. For example, the braking condition, in response to which thevehicle may have begun braking at the predetermined barking rateprofile, may cease to exist before the vehicle reaches its maximumbraking rate capability and the vehicle may cease braking in response.

Consistent with this disclosure, the at least one processing device maybe configured to implement the planed navigational action if thedetermined host vehicle stopping distance is less, by at least apredetermined minimum distance, than the determined next-state distancesummed together with a target vehicle travel distance determined basedon the current speed of the target vehicle and the assumed maximumbraking rate capability of the target vehicle. In some embodiments, theminimum distance may be d_(min) as discussed above in relation to CRSSand RSS and may be predetermined or determined by any means consistentwith this disclosure. In some embodiments, the predetermined minimumdistance may correspond to a predetermined separation distance to bemaintained between the host vehicle and other vehicles. For example, ifa host vehicle and a target vehicle are traveling in the same directionand both come to a stop, the predetermined separation distance may bethe minimum distance between the host vehicle and the target vehicleafter both come to a stop. The predetermined separation distance may bea distance of any length. For example, the predetermined separationdistance may be at least 1 m or other suitable minimum approachdistance. In some embodiments, the predetermined distance may varydepending upon, for example, the speed at which the host vehicle istraveling, the location of the host vehicle (e.g., an urban road, arural highway, etc.). For example, the d_(min) may increase as hostvehicle speed increases.

The embodiments discussed in relation to CRSS are exemplary only. One ofordinary skill in the art having the benefit of this disclosure mayunderstand that CRSS may be used instead of or in association with RSSin any of the embodiments discussed in this disclosure. In someembodiments, a host vehicle may be capable of navigating under eitherthe CRSS or RSS modes. For example, a fully autonomous vehicle may beconfigured to navigate under the rules of the CRSS model, but apassenger in the vehicle may disengage the CRSS model and choose tonavigate under the RSS mode. Such a mode selection, for example, mayenable the host vehicle to approach target vehicles more closely, whilestill maintaining a safe distance. The tradeoff, however, is that theRSS mode may be associated with higher deceleration rates than the CRSSmode and may be less comfortable to the passengers of the host vehicle.In some embodiments, an autonomous vehicle may be capable of navigatingunder each of the CRSS and RSS modes. For example, the vehicle may beconfigured to employ the CRSS model when traveling under firstconditions (e.g., at high speeds, on a rural highway, etc.) and the RSSmode when traveling under second conditions (e.g., at low speeds, on anurban highway, etc.).

Consistent with this disclosure, the CRSS mode may be used to navigate afully autonomous vehicle, may be used to navigate a partially autonomousvehicle (e.g., a vehicle with a human-operable mode and a selectivelyautonomous mode), or may be used as an underlying safety feature in ahuman operable vehicle (e.g., a human-operable vehicle may prevent oravoid situations that may be unsafe under the CRSS model).

Vision Zero Safety System for a Driver-Operated Vehicle

In some embodiments, a safety system (e.g., Vision Zero) may be employedin a host vehicle having autonomous or partially autonomouscapabilities, but for which a human driver is allowed to operate in adriver-controlled mode. In such cases, the safety system can operate inthe background. The human driver may be allowed to take any navigationalaction he or she wishes as long as the navigational action does notresult in less than a CRSS or RSS distance relative to detected targetvehicles. If the driver never takes a navigational action that wouldresult in an approach relative to a target vehicle of less than the CRSSor RSS distance (depending on the selected mode of operation, forexample), then the human driver may be unaware of the operation of thesafety system. On the other hand, if a driver initiates a navigationalaction that would result in an approach relative to a target vehicle ofless than a CRSS or RSS distance, then the safety system will take oneor more actions to prevent the initiated navigational action from beingcompleted. In other words, the vehicle may take control of the vehiclefrom the driver to avoid navigation into an unsafe situation involvingan approach distance less than CRSS or RSS. The driver retakes controlonce he or she aborts attempts to navigate into a condition the vehiclesenses as unsafe or when the driver initiates a different navigationalaction deemed by the host vehicle to be safe.

The disclosed safety system may take control of the vehicle to prevent anavigation action, may prevent a driver input associated with apotentially unsafe navigational action (e.g., one detected as having aresult that would violate a CRSS or RSS envelope), inhibit certainnavigational inputs, alert a driver, and/or a combination thereof. Forexample, the safety system may prevent a lateral motion of the vehicleif it would result in an unsafe cut-in (e.g., if the vehicle would cutin front of a target vehicle such that the distance between the vehicleand the target vehicle is less than the RSS safe distance). An exampleof an unsafe cut-in that may be prevented by the safety system isdepicted in FIG. 30A. As another example, the safety system may preventa navigational action that would result in a longitudinal motion that,in turn, would result in less than an RSS or CRSS distance between thehost vehicle and a target vehicle (e.g., a leading target vehicle). Anexample of an unsafe longitudinal motion that may be prevented by thesafety system is depicted in FIG. 28B. As another example, the safetysystem may prevent lateral or longitudinal motion of the host vehicle(in response to a driver input) that would result in less than apredetermined distance or a safe distance between the host vehicle and apedestrian. Examples of unsafe motion relation to pedestrians that maybe prevented by the safety system are depicted in FIGS. 44A and 44C.

Consistent with this disclosure, the safety system may prevent a humandriver's attempted navigational maneuvers if they are unsafe. As usedherein, “prevent” may include any means for making a human driver unableto perform the navigational maneuver. For example, if the unsafenavigational maneuver is a merge, the safety system may stop the mergeby locking the steering wheel or other steering mechanism (e.g., suchthat the steering wheel cannot be turned in the direction of the merge),by applying an equal but opposite steering input to cancel out thedriver's steering input, by intercepting or interrupting an electricalsignal associated with a driver's steering input, or otherwise cause thedriver's steering input to have no navigational response or less thanthe intended navigational response. As another example, if the unsafenavigational maneuver is an acceleration, the safety system may stop theacceleration by causing an acceleration input to have no effect (e.g.,interception of an electric signal, locking the gas-pedal, applying thebrake, etc.). The prevention may be sufficient to avoid or stop anavigational maneuver that would otherwise be unsafe (e.g., one that isdetermined to have a resulting approach to a target vehicle less thanCRSS or RSS, etc.).

Consistent with this disclosure, the safety system may take over avehicle to avoid an unsafe navigational maneuver attempted by a humandriver. During a takeover period, the safety system may operate in anautonomous mode and fully control the host vehicle, until, for example,it is determined that a driver input would no longer result in an unsafenavigational action. As used herein, “take over” may include anyoperation of one or more autonomously controlled actuators by which thesafety system may manipulate or control one or more of the steering,braking, acceleration, or other vehicle control systems. For example, ifa driver input is determined to be associated with an unsafe merge, thesafety system may temporarily take control of the steering mechanism ofthe vehicle such that the driver cannot provide additional steeringinput to cause the merge or so that a driver's input has no effect andthe safety system may steer the vehicle in a direction to avoid theunsafe maneuver (e.g., counter steer against the initiated driver inputon the steering wheel). As another example, if the unsafe maneuver is anacceleration, the safety system may take control of the accelerationmechanism such that the driver cannot provide additional input to thethrottle, for example, or such that the driver's input has no effect andthe safety system may decelerate, maintain the current speed, or causethe vehicle to coast to avoid the unsafe conditions. The safety systemtake over is designed to avoid navigational maneuvers that aredetermined by the system to be unsafe and to avoid collisions,especially those that may be the fault of the host vehicle.

As used herein, the term “displace,” when used to refer to the safetysystem displacing a human driver, may refer to any of inhibiting,preventing, or taking control from the human driver.

As noted, the autonomous safety system may operate in the backgrounduntil an unsafe condition or a driver input determined to be associatedwith an unsafe maneuver is detected. In such cases, the safety systemmay displace human driver control (at least temporarily). The unsafecondition may include, for example, a determination that a driver inputis associated with a navigational maneuver that would place a hostvehicle a distance from a target vehicle that is less than the CRSS orRSS safe distance. As an example, a processing device of the safetysystem may use the longitudinal and/or lateral safe distances developedunder the RSS model and/or the CRSS model to construct a proximitybuffer relative to the host vehicle (or detected target vehicles), Inthis example, a safe condition may include any condition where there isno object (e.g., target vehicle or VRU) within the proximity buffer.Conversely, an unsafe condition may include any condition where there isor would be an object within the proximity buffer. The proximity buffermay include a two-dimensional or three-dimensional area around a hostvehicle. The dimension of the proximity buffer may be determined usingthe RSS and/or CRSS safe distance calculations described above. Forexample, a proximity buffer may include a distance in front of the hostvehicle corresponding with, for example, a CRSS safe longitudinaldistance or an RSS distance; a distance on either side of the hostvehicle corresponding with, for example, a predetermined safe lateraldistance; and/or a distance in the rear of the host vehiclecorresponding with, for example, an RSS safe distance.

FIGS. 52A-52D are visual representations of exemplary proximity buffersconsistent with this disclosure. FIG. 52A depicts proximity buffer 5202around host vehicle 5201. In this example, proximity buffer 5202 isderived from a determined safe distance 5204 in front of host vehicle5201 and from a determined safe distance 5206 behind host vehicle 5201.Determined safe distance 5204, which is the shortest safe distance amongthe examples of FIGS. 52A-52D, may be an RSS longitudinal safe distance.Accordingly, determined safe distance 5204 may be determined asdescribed above. Similarly, determined safe distance 5206 may be an RSSlongitudinal safe distance. The lateral safe distances that comprise thesides of proximity buffer 5202, are not labeled, but it is understoodthat they may be determined by any means consistent with thisdisclosure. Such lateral safe distances may be predetermined in order tomaintain a minimum lateral spacing between the host vehicle and othervehicles or objects. Such a lateral safe distance may be 0.25 m, 0.5 m,1.0 m, or more for example. In some embodiments, the sides of theproximity buffer may correspond with a predetermined lateral distancethreshold, which may define a minimum safe lateral distance between ahost vehicle and an object.

FIG. 52B depicts proximity buffer 5212 around host vehicle 5211. In thisexample, determined safe distance 5214 in front of host vehicle 5211 islonger than determined safe distance 5204 in front of host vehicle 5201.In some embodiments, determined safe distance 5214 may be longer than5204 because, for example, determined safe distance 5214 may correspondto a CRSS safe distance. Determined safe distance 5214 may alsocorrespond with an RSS safe distance together with a minimum approachdistance, as described above. As noted above, determined safe distance5214 may correspond with a CRSS safe distance that includes a brakingdistance associated with a sub-maximal braking rate. In someembodiments, determined safe distance 5214 may be longer than determinedsafe distance 5204 because host vehicle 5211 may have different brakingcharacteristics or features, etc., as compared to host vehicle 5201. Forexample, both determined safe distance 5204 and determined safe distance5214 may be an RSS safe distance and determined safe distance 5214 maybe longer because host vehicle 5211 may be associated with a highercurrent speed and/or a lower maximum braking capability as compared tohost vehicle 5211.

FIG. 52C depicts proximity buffer 5222 around host vehicle 5221. In thisexample, determined safe distance 5224 is longer than determined safedistance 5204 and shorter than determined safe distance 5214. In someembodiments, determined safe distance 5224 may be shorter thandetermined safe distance 5214 and longer than determined safe distance5204 for any of the reasons described in relation to FIG. 52B. Forexample, determined safe distance 5224 may be an RSS safe distance thatincludes a minimum approach distance, as described in relation to theRSS model, but the maximum acceleration capability of host vehicle 5221may be less than that of host vehicle 5211 and/or the predeterminedapproach distance may be less for host vehicle 5221 than for hostvehicle 5211. As another example, a passenger or driver of host vehicle5221 may have selected a first sub-maximal braking rate and a passengeror driver of host vehicle 5211 may have selected a second sub-maximalbraking rate that is less than that of the first sub-maximal brakingrate and, therefore, host vehicle 5211 may require a greater distance(e.g., determined safe distance 5214) to come to a stop safely. In thisexample, host vehicle 5221 has a longer determined safe distance 5226behind the vehicle. Like determined safe distance 5224 in the front ofhost vehicle 5221, the length of determined safe distance 5226 may belonger than determined safe distance 5216 due to the model used todetermine the distance (e.g., RSS and/or CRSS), a condition orcharacteristic of host vehicle 5221 (e.g., maximum accelerationcapability, maximum braking capability, current speed, current brakingcapability, sub-maximal braking rate, etc.), and/or a condition of theroad (e.g., a weather condition, a material of the road, etc.).

FIG. 52D depicts proximity buffer 5232 around vehicle 5231. Proximitybuffer 5232 is larger than any of proximity buffer 5205, 5212, or 5222.In some embodiments, proximity buffer 5232 may larger than the otherbuffers because, for example, the CRSS model was used for bothdetermined safe distance 5234 in the front of host vehicle 5231 and fordetermined safe distance 5236 behind host vehicle 5231. In someembodiments, the size of proximity buffer 5232 may be due to any of thefactors discussed in relation to FIGS. 52A-52C.

Consistent with this disclosure, a host vehicle may have more than oneproximity buffer. For example, a host vehicle may have a first proximitybuffer associated with the RSS model (e.g., proximity buffer 5202) and asecond proximity buffer associated with the CRSS model (e.g., proximitybuffer 5232). In some embodiments, the safety system may displace ahuman driver if the first proximity buffer is breached. For example, ifa host vehicle comes within a distance to a target vehicle that is lessthan the RSS safe distance, the safety system may displace the driver toprevent a collision. In the same embodiments, the safety system mayalert the human driver if the second proximity buffer is breached butforego displacing the driver. For example, if a host vehicle comeswithin a distance of a target vehicle that is less than the CRSS safedistance, the safety system may alert the driver that the host vehicleis too close to the target vehicle by, for example, transmitting anaudible warning over a speaker system; causing a seat, steeringmechanism, or other component in a passenger compartment to vibrate;displaying an alert on a heads-up display or augmented reality display;or by any other means. In some embodiments, the safety system maydisplace the human driver if the second proximity buffer is breached.For example, if a host vehicle comes within a distance of a targetvehicle that is less than a CRSS safe distance, the safety system maycause the vehicle to decelerate at a rate corresponding with thesub-maximal braking rate of the CRSS model. If the distance between thehost vehicle and the target vehicle breaches the first proximity bufferby becoming closer than the RSS safe distance, the safety system maycause the vehicle to decelerate at a rate corresponding with the maximalbraking rate of the host vehicle according to the RSS model. And, asdescribed above, the safety system may also displace the human driverany time an input from the driver is determined as one that would causean approach relative to another vehicle or an object less than an RSS orCRSS distance.

As described above, each of the RSS and CRSS models may calculate safedistances that are relative to the detected object. For example, eachmodel may determine a braking capability of a target vehicle and usethat braking capability to determine a safe distance. As such, thedimension of the proximity buffer may be different depending on theobject detected in the environment of the host vehicle. As an example,an RSS safe distance between a host vehicle and a first target vehiclemay be longer than the RSS safe distance between the host vehicle and asecond target vehicle when the second target vehicle has a highermaximum braking capability than the first target vehicle (i.e., thesecond target vehicle may come to a stop in a shorter distance than thefirst target vehicle). As another example, an RSS or CRSS safe distancebetween a host vehicle and a pedestrian may be significantly longer thanan RSS or CRSS safe distance between the host vehicle and any targetvehicle because the minimum separation distance between the host vehicleand the pedestrian may be larger than that of the host vehicle and atarget vehicle.

The safety system may displace the human driver for a durationcorresponding with the unsafe condition, such as a breach of a proximitybuffer or during a time period in which an unsafe driver input isdetected (e.g., at least one driver input determined as one that wouldcause an approach relative to another vehicle or an object less than anRSS or CRSS distance), For example, the safety system may take controlof the vehicle until the unsafe condition ceases to exists (e.g., thevehicle is a distance from a target vehicle that is larger than the CRSSor RSS safe distance).

FIGS. 53A and 53B illustrate examples of safe and unsafe conditionsbetween two vehicles. FIG. 53A depicts host vehicle 5301 and targetvehicle 5303 traveling in a common direction along roadway 5302. In thisexample, host vehicle 5301 may include a safety system consistent withthis disclosure and a proximity buffer 5304. Similarly, target vehicle5303 may include a safety system consistent with this disclosure andhave a proximity buffer 5306. In this example, if host vehicle 5301 isdriven by a human driver, the human driver may continue navigating hostvehicle 5301 (e.g., the human driver will not be displaced by the safetysystem), because there are no objects within proximity buffer 5304. Thesame may be true of a human driver navigating target vehicle 5303.

FIG. 53B depicts host vehicle 5311 and target vehicle 5313 traveling ina comet ion direction along roadway 5312, In this example, host vehicle5301 may include a safety system consistent with this disclosure and aproximity buffer 5314. Similarly, target vehicle 5313 may include asafety system consistent with this disclosure and have a proximitybuffer 5316. In this example, if host vehicle 5311 is driven by a humandriver, and the safety system of target vehicle 5313 detects a driverinput determined to be one (or more) that would result in the cut-inshown in FIG. 53B, the safety system may displace the human driver andtake control to prevent the action. For example, the safety systemassociated with vehicle 5313 may determine that the driver input wouldresult in a situation in which a lateral safe distance may be breached,insufficient longitudinal spacing to the rear of vehicle 5313 wouldresult after the maneuver (e.g., an RSS distance would not exist afterthe cut-in), etc. In such cases, the safety system would respond bypreventing the driver input from resulting in the unsafe cut-inmaneuver. In the same scenario of FIG. 53B, if vehicle 5313 did make thecut-in maneuver, the safety system of vehicle 5311 may displace thedriver input, for example, if the driver did not brake to slow thevehicle in order to establish a CRSS or RSS distance associated withbuffer 5314. In such situations, the unsafe driver input may correspondto a lack of change in input or, in other words, and unsafe maintainingof current input/control.

FIGS. 54A and 54B illustrate additional instances where a safety systemconsistent with this disclosure may displace a human driver. In FIGS.54A and 54B, vehicle 5402, vehicle 5404, and vehicle 5406 are eachtraveling in a common direction on roadway 5400. In this example,roadway 5400 may be a highway. Vehicle 5402 may include a safety systemconsistent with this disclosure and may have a proximity buffer 5403.Proximity buffer 5403 may correspond with any of the RSS and/or CRSSmodels, as discussed above. For the purposes of illustration, proximitybuffer 5403 is assumed to have a determined safe distance in the frontof vehicle 5402 associated with the CRSS model.

In FIG. 54A, a human driver in vehicle 5402 may cause vehicle 5402 toapproach the rear of vehicle 5406 as shown. If the driver attempts tocause vehicle 5402 to come within a distance of vehicle 5406 that isless than the CRSS safe distance (as shown by vehicle 5406 being withinproximity buffer 5403), the safety system of vehicle 5402 may displacethe driver to avoid an unsafe condition and to maintain the CRSSdistance. For example, the safety system may take control and prevent orignore the driver's acceleration input or may brake vehicle 5402. Forexample, the safety system may cause vehicle 5402 to decelerate at arate corresponding with the sub-maximal braking rate of the CRSS modeluntil vehicle 5402 is a distance from vehicle 5406 that is greater thanproximity buffer 5402. As another example, before proximity buffer 5403is breached, the safety system may determine a next-state position ofvehicle 5402 (e.g., the position vehicle 5402 would be in if thedriver's input were executed) and may displace the driver before vehicle5402 is brought within a distance of vehicle 5406 that is less than theCRSS safe distance.

In FIG. 54B, a human driver in vehicle 5402 may attempt to cause vehicle5402 to merge into the lane occupied by vehicle 5404. If the driverattempts a navigational action that may cause vehicle 5402 to comewithin a distance of vehicle 5404 that is less than the CRSS safedistance (as shown by the overlap between proximity barrier 5403 andvehicle 5404), the safety system may displace the human driver toprevent the navigational action. For example, if the human driverattempts to veer to the right, for example, by turning a steering Wheelto the right, the safety system may determine that execution of the veerwould result in the unsafe condition shown in FIG. 54B. The safetysystem may, in response, take over control and displace the humandriver. For example, the safety system may inhibit the turning of thesteering wheel to the right by exhibiting an equal force on the steeringwheel to the left. As another example, the safety system may prevent theright veer by causing the right turn of the steering wheel to have noeffect through mechanical and/or electrical interruption of the rightturn input. As another example, the safety system may take over vehicle5402 and steer to the left as needed to avoid the unsafe conditions thatwould arise if the right veer were executed. For any of these examples,the displacement may last until vehicle 5402 is retuned to safeconditions (e.g., to a position where neither of vehicles 5404 or 5406are within proximity barrier 5403) and/or a next-state conditionassociated with vehicle 5402 is determined to be safe.

The examples depicted in FIGS. 53A-53B and 54A-54B are exemplary only.One of skill in the art having the benefit of this disclosure mayunderstand that a safety system or similar navigational system maydisplace a human driver in any unsafe condition or in response to anyinput that may cause an unsafe condition.

In some embodiments, the safety system may store or transmit datarelating to any instances wherein the safety system displaced the humandriver. For example, the safety system may generate data relating to theunsafe condition that caused the safety system to displace the driver,the type of displacement that occurred (e g inhibition, prevention, ortake over), the duration of the displacement, the outcome of thedisplacement (e.g., vehicle returned to safe conditions, vehiclestopped, vehicle involved in collision), or any other informationrelating to the displacement or the events occurring before or after thedisplacement. Consistent with this disclosure, the information may beused to determine whether the safety system, the RSS model, the CRSSmodel, or any other autonomous vehicle feature is performing aspredicted. Such information may be transmitted from the host vehicle toa remote server over one or more networks. For example, the informationmay be transmitted to the automobile manufacturer, the safetymanufacturer, or other party responsible for implementing the safetysystem for analysis. In some embodiments, the information may bedisplayed to the driver of the vehicle. For example, a report may begenerated after each displacement event, after each trip, afterreceiving a request from the driver, or on a scheduled interval (e.g.,daily, weekly, bi-weekly, monthly, etc.). It is contemplated thatproviding the driver information relating to the safety system and theunsafe conditions avoided may increase the amount of trust the driverhas in the safety system (or in autonomous vehicles generally).

In some embodiments, the vehicle may include a means (e.g., switch,button, voice activated control, or other type of control) fordeactivating or disengaging the safety system. For example, a driver maydeactivate the safety system to prevent it from disengaging the driveror a driver may disengage the safety system during a displacement eventto retake control of the host vehicle. It is contemplated that thecontrol for deactivating or disengaging the safety system be independentfrom any of the control mechanisms of the vehicle associated withnavigating the vehicle. For example, the vehicle may include a buttonthat is not associated with the throttle, brake, steering wheel, or anyother control mechanisms. In this example, the driver may onlydeactivate or disengage the safety system by pressing the button (orother safety system control). Unlike traditional ADAS systems (i.e.,advanced driver assist systems such as lane-keeping systems, autobraking systems, etc.), the disclosed safety system cannot be deactivateor disengaged by providing an input to a steering control, a brakingcontrol, or a throttle control. For example, if the safety system takesover the steering mechanism of the vehicle in order to perform a rightturn, the driver cannot disengage the safety system by, for example,continuing to turn the wheel to the right (e.g., with an increase inforce in an attempt to overcome or disengage the safety system). Rather,the driver would first need to activate the designated safety systemoverride control to disengage the safety system. Similarly, if thedisclosed safety system takes control to prevent a navigational actionthat would result in a longitudinal distance less than CRSS or RSS, thedriver would not be able to override the safety system with input to thevehicle brake or throttle. Rather, the designated safety system controlwould need to be used.

It is understood that the safety system may be disengaged or deactivatedby any appropriate control input, such as a lever, a knob, a virtualbutton, a voice command, a hand gesture, or the like. In someembodiments, the navigation system may include an image capture deviceinside the vehicle, which is configured to capture one or more images orvideos of a human driver. At least one processing device may analyze thecaptured images and/or videos to recognize a hand gesture or othernon-verbal command and may be programmed to deactivate or disengage thesafety system in response to the hand gesture or other non-verbalcommand. In some embodiments, the navigation system may include one ormore microphones configured to capture sound data. The at least oneprocessing device may analyze the sound data using voice recognitionprocessing (e.g., using a neural network, a trained or untrained system,etc.) and deactivate or disengage the safety system in response to sounddata including a recognized command.

Consistent with this disclosure, the safety system may collectinformation relating to any instances where the safety system isdeactivated or disengaged. For example, the safety system may record thenavigational circumstances just prior to a deactivation of the safetysystem (e.g., the speed, acceleration, following distance, etc. of thehost vehicle) and/or the time and place of the deactivation. In someembodiments, the safety system may continue to monitor the drivingconditions of the driver even after it has been deactivated ordisengaged and to store or transmit that data as described above.

Consistent with this disclosure, a navigation system for selectivelydisplacing human driver control is disclosed. The navigation system maypartially displace the driver, for example by preventing or inhibitingan action of the driver, or may fully displace the driver, for exampleby taking over the vehicle and performing navigational maneuversindependent from the driver. The navigation system may be a safetysystem or any other system disclosed herein. In some embodiments, thesystem may be fully housed within a host vehicle. In other embodiments,one or more components of the system may be located in a location remotefrom the host vehicle, such as in a server or other device. The systemmay include at least one processing device. The at least one processingdevice may be programmed to perform one or more methods, processes,operations, or functions consistent with this disclosure. The at leastone processing device may be, for example, processing device 110.

FIG. 55 is a flowchart depicting exemplary process 5500 for selectivelydisplacing a human driver. Consistent with this disclosure, the at leastone processing device in the navigational system may be programmed toperform all or part of process 5500. Process 5500 is exemplary only andone of ordinary skill in the art having the benefit of this disclosuremay understand that process 5500 may include additional steps, mayexclude one or more steps, or may be otherwise modified in waysconsistent with this disclosure.

Process 5500 may include a step 5502 for receiving one or more images.The at least one image may represent, for example, the environment of ahost vehicle. In some embodiments, the processing device may beprogrammed to receive at least one image representative of anenvironment of the host vehicle. The at least one image may be receivedfrom at least one image capture device. For example, the navigationsystem may include one or more image capture devices, such as imagecapture device 122, which may capture an image of the environment of thehost vehicle. The image capture device may have a field of viewcorresponding with a field of view of the human driver. In someembodiments, the navigation system may include a plurality of imagecapture devices, each having a different field of view relative to theenvironment of the host vehicle. For example, at least one of theplurality of image capture devices may be configured to capture imagesrepresentative of the environment of the host vehicle to a rear of thehost vehicle; at least one of the plurality of image capture devices maybe configured to capture images representative of the environment of thehost vehicle to a side of the host vehicle; and/or at least one of theplurality of image capture devices may be configured to capture imagesrepresentative of the environment of the host vehicle in front of thehost vehicle; and so forth. For example, a first image capture devicemay have a field of view corresponding with an area in front of the hostvehicle, a second image capture device may have a field of viewcorresponding with the right side of the host vehicle, and so forth. Inthe disclosed embodiments, the processing device may be programmed toreceive a plurality of images. For example, in embodiments where thenavigation system contains only one image capture device, the processingdevice may receive a plurality of images from the imaging device. Asanother example, the processing device may receive one or more imagesfrom a first image capture device and/or one or more images from asecond image capture device, one or more imaged from a third imagecapture device, and so forth.

Process 5500 may include a step 5504 for detecting at least one obstaclein the environment of the host vehicle. The at least one obstacle may bedetected by analysis of at least one image. The at least one image maybe one or more images received at step 5502. For example, the processingdevice may be programmed to detect at least one obstacle in theenvironment of the host vehicle based on analysis of the at least oneimage. For example, the processing device may compare a received imagewith one or more images of known obstacles, or may detect shapes, text,or other objects in the image that correspond with one or moreobstacles. The one or more obstacles may be any object in theenvironment of the host vehicle. For example, the one or more obstaclesmay be target vehicles or VRUs on or near a road on which the hostvehicle is traveling. As another example, the one or more obstacles maybe pot holes, railings, road signs, traffic lights, traffic cones,railings or barriers, or any other object on or along a road way. Insome embodiments, a plurality of obstacles may be detected in theenvironment of the host vehicle. For example, the processing device maydetect a first host vehicle, a second host vehicle, a traffic light, apot hole, and any number of additional obstacles.

In embodiments in which the navigation system includes a plurality ofimage capture devices, each of which may have a different field of viewrelative to the environment of the host vehicle, the at least oneprocessing device may be configured to receive one or more images fromeach of the plurality of image capture devices and to detect at leastone obstacle in the environment of the host vehicle based on analysis ofthe one or more images received from the plurality of image capturedevices. For example, at least one of the plurality of image capturedevices may be configured to capture images representative of theenvironment of the host vehicle to a side of the host vehicle and one ormore images received from that image capture device may be used todetect one or more obstacles located to the side of the host vehicle.Similarly, at least one of the plurality of image capture devices may beconfigured to capture images representative of the environment of thehost vehicle to a rear of the host vehicle and one or more imagesreceived from that image capture device may be used to detect one ormore obstacles located behind the host vehicle.

In some embodiments, the at least one obstacle may be a target vehiclein the environment of the host vehicle. For example, the at least oneobstacle may be a target vehicle that is determined to be forward of thehost vehicle. As another example, the at least one obstacle may be atarget vehicle determined to be in a lane different from the hostvehicle. In some embodiments, the at least one obstacle may include apedestrian or object in the roadway.

In some embodiments, the processing device may detect one or moreobstacles in the environment using the outputs from one or more sensorsassociated with the host vehicle. The sensors may be any sensorsdisclosed herein. For example, the processing device may receive anoutput from a LIDAR system and/or a RADAR system and use thatinformation to detect one or more obstacles in the vicinity of the hostvehicle.

Process 5500 may include a step 5506 for monitoring driver input into athrottle mechanism, a braking mechanism, and/or a steering mechanism.Consistent with this disclosure, the at least one processing device maybe programmed to monitor a driver input to at least one or a throttlecontrol, a brake control, or a steering control associated with the hostvehicle. The input may be monitored by any technique consistent withthis disclosure. For example, one or more sensors may be configured todetect an electrical signal associated with any of the throttle, brake,or steering controls. In another example, one or more sensors may beconfigured to detect a mechanical input to any of the throttle, brake,or steering controls. The throttle control, brake control, and/or thesteering control may be of any type presently known or subsequentlydeveloped. For example, the throttle control may include an acceleratorpedal, the brake control may include a brake pedal, and the steeringcontrol may include a steering wheel. In another example, one or morehost vehicle control systems may include at least one steering actuatorto control a heading of the host vehicle, a braking actuator to causeapplication of a host vehicle braking device, or an accelerationactuator to cause application of a host vehicle throttle. For example,the throttle control system may include an acceleration actuator tocause application of the host vehicle throttle, the brake control systemmay include a braking actuator to cause application of the host vehiclebrake pedal, and/or the steering control system may include at least onesteering actuator to control a heading of the host vehicle. The driverinput may be any active movement or other activation of one or more ofthe controls or an absence of movement or other activation. Continuingthe above example, the driver input may include at least one adepression of the acceleration pedal, a depression of the brake pedal, alack of depression of the brake pedal, a rotation of the steering wheel,or a non-rotation of the steering wheel.

Process 5500 may include a step 5508 for determining whether the driverinput would result in a safe navigational action. As described, thedriver input may result in safe conditions if the navigational changethat would occur if the driver input were given effect would not causethe host vehicle to come within a distance from an object that is lessthan the proximity buffer around the host vehicle (e.g., within an RSSdistance, a CRSS distance, or a predetermined minimum lateral bufferdistance, among others). Consistent with this disclosure, the at leastone processing device may be programmed to determine whether the driverinput would result in the host vehicle navigating within a proximitybuffer relative to the at least one obstacle. The at least oneprocessing device may determine whether a proximity buffer may bebreached by any techniques consistent with this disclosure. For example,the processing device may determine a current distance between the hostvehicle and one or more objects (e.g., target vehicle or VRUs) anddetermine a next-state distance between the host vehicle and the one ormore Objects based on the current distance and the driver input. Suchdistances between objects may be determined, for example, based imageanalysis (e.g., scaling Observations), LIDAR output, RADAR output, etc.As an example, referring to FIGS. 53A and 53B, if a human driverprovides an input that would cause vehicle 5303 to veer left (e.g., byrotating a steering wheel of vehicle 5303), the processing device maydetermine that the next-state distance between vehicle 5303 and vehicle5301 would be the unsafe condition depicted in FIG. 53B. As anotherexample, referring to FIG. 54A, if a human driver of vehicle 5402provides an acceleration input (e.g., by depressing an accelerationpedal), the processing device may determine that an acceleration ofvehicle 5402 may cause vehicle 5402 to come within a distance of vehicle5406 that is less than proximity buffer 5403 and is, therefore, unsafe.In such cases, the safety system may take control of the host vehicleand prevent the unsafe maneuver associated with the detected driverinput.

Process 5500 may include a function 5510 that may dictate how thenavigational system handles instances where the driver input would causea host vehicle to breach a proximity buffer and instances where thedriver input would not cause the host vehicle to breach a proximitybuffer. In some embodiments, function 5510 may be include in step 5508of process 5500. The proximity buffer may be any proximity bufferconsistent with this disclosure, including those determined using theRSS and/or CRSS models. The proximity buffer may depend upon thedetected obstacle or object in the environment of the host vehicle onwhich the RSS and CRSS models depend. In some embodiments, the proximitybuffer may include one or more predetermined distances. For example, theproximity buffer may correspond with a predetermined lateral distancethreshold. The lateral distance threshold may include a predeterminedminimum distance between a host vehicle and an object located on eitherside of the host vehicle. As another example, the proximity buffer maycorrespond with a predetermined longitudinal distance. The longitudinaldistance may be, for example, minimum distance d_(min) that is to bemaintained between the host vehicle and an object, as described withrespect to the RSS model.

Consistent with this disclosure, the at least one obstacle may include atarget vehicle, and the proximity buffer relative to the target vehiclemay be determined based on a detected current speed of the host vehicle,a maximum braking rate capability of the host vehicle, a determinedcurrent speed of the target vehicle, an assumed maximum braking ratecapability of the target vehicle, and a determined maximum accelerationcapability of the host vehicle. In such cases, the proximity buffer mayinclude at least a sum of a host vehicle acceleration distance,determined as a distance over which the host vehicle will travel ifaccelerated at the maximum acceleration capability of the host vehicleover a reaction time associated with the host vehicle; a host vehiclestopping distance, determined as a distance required to reduce thecurrent speed of the host vehicle to zero at the maximum braking ratecapability of the host vehicle; and a target vehicle stopping distance,determined as a distance required to reduce the current speed of thetarget vehicle to zero at the assumed maximum braking rate capability ofthe target vehicle. For example, the proximity buffer may be determinedusing an RSS safe distance, which includes the acceleration distance andthe stopping distance of the host vehicle as well as the stoppingdistance of the target vehicle. In some embodiments, the proximitybuffer relative to the target vehicle may further be determined based ona predetermined minimum distance to be maintained between the hostvehicle and the target vehicle. For example, the proximity buffer mayinclude minimum distance d_(min) as discussed above.

Consistent with this disclosure, the at least one obstacle may include atarget vehicle, and the proximity buffer relative to the target vehiclemay be determined based on a detected current speed of the host vehicle,a maximum braking rate capability of the host vehicle, a determinedcurrent speed of the target vehicle, an assumed maximum braking ratecapability of the target vehicle, and a maximum acceleration capabilityof the host vehicle. In some embodiments, the proximity buffer relativeto the target vehicle may be further determined based on a predeterminedsub-maximal braking rate that is less than the maximum braking ratecapability of the host vehicle, such that the proximity buffer includesat least a sum of a host vehicle stopping distance, determined as adistance required to reduce the current speed of the host vehicle tozero at the predetermined sub-maximum braking capability of the hostvehicle, and a target vehicle stopping distance, determined as adistance required to reduce the current speed of the target vehicle tozero at the assumed maximum braking capability of the target vehicle.For example, the proximity buffer may be determined using a CRSS safedistance, which include a stopping distance of the host vehicle if thehost vehicle decelerates at a rate corresponding with a predeterminedsub-maximal braking rate and a stopping distance of the target vehicleif the target vehicle decelerates at a rate corresponding with itsmaximum braking rate capability. In some embodiments, the proximitybuffer relative to the target vehicle may further be determined based ona predetermined minimum distance to be maintained between the hostvehicle and the target vehicle. For example, the proximity buffer mayinclude minimum distance d_(min) as discussed above.

In any of the embodiments disclosed above, the target vehicle may be infront of, next to, or behind the host vehicle. For example, the targetvehicle may be forward of the host vehicle and the at least oneprocessing device may be configured to determine that a driver inputcould result in a change in the longitudinal distance between the targetvehicle and the host vehicle. For example, the host vehicle may be adistance from the target vehicle that is greater than the distance ofthe proximity buffer in front of the host vehicle and the driver inputmay cause the host vehicle to be a distance from the target vehicle thatis less than the distance of the proximity buffer. In some embodiments,the target vehicle may be determined to be in a lane different from thehost vehicle, and the at least one processing device may be configuredto determine that the driver input would result in a lateral movement ofthe host vehicle, such that after the lateral movement, the targetvehicle will be forward of the host vehicle. For example, the driverinput may cause the host vehicle to merge behind a target vehicle, whichmay be safe if the host vehicle would retain a distance from the targetvehicle that is greater than the distance of the proximity buffer infront of the host vehicle and may be unsafe it the host vehicle wouldcome within a distance of the target vehicle that is less than thedistance of the proximity buffer in front of the host vehicle. In someembodiments, the target vehicle is determined to be in a lane differentfrom the host vehicle, and the at least one processing device isconfigured to determine that the driver input would result in a lateralmovement of the host vehicle, such that after the lateral movement, thehost vehicle will be forward of the target vehicle. For example, thedriver input may cause the host vehicle to cut-in in front of a targetvehicle, which may be safe if the host vehicle would retain a distancethat is greater than the proximity buffer in the rear of the vehicle ormay be unsafe if the host vehicle would come within a distance of thetarget vehicle that is less than the proximity buffer in the rear of thehost vehicle.

Consistent with this disclosure, the at least one obstacle may include apedestrian or an object in a roadway, and the proximity buffer relativeto the at least one obstacle may include at least a minimum distance tobe maintained between the host vehicle and the at least one obstacle. Asdiscussed above, the minimum distance may vary depending on theclassification of the obstacle. For example, if the obstacle is apedestrian, the minimum distance may be a distance at which there is acertainty, within a predetermined threshold, that the host vehicle willbe able to avoid a collision with the pedestrian. As such, the minimumdistance relative to a pedestrian may be the longest minimum approachdistance consistent with this disclosure. In some embodiments, theproximity buffer relative to a pedestrian may be determined based on acurrent speed of the host vehicle, and the proximity buffer may increasewith increasing host vehicle speed. Even in instances where theproximity buffer relative to a pedestrian is based on a current speed ofthe host vehicle, it is contemplated that the proximity buffer relativeto the pedestrian would be longer than a stopping distance (andgenerally, significantly longer than a stopping distance) of the hostvehicle. For example, a proximity buffer relative to a pedestrian may bea stopping distance of the host vehicle (calculated under the P.S.S orCRSS models) for a current speed of the host vehicle plus an additionalminimum distance. As another example, a proximity buffer relative to apedestrian may be 120% of a stopping distance of the host vehicle for acurrent speed of the host vehicle, or a different modification to thestopping distance (e.g., 110%, 150%, 200%, etc.).

Process 5500 may include a step 5514 for allowing the driver input ifthe input would not cause the host vehicle to come within a proximitybuffer relative to an object. Consistent with this disclosure, the atleast one processing device may be programmed to allow the driver inputto cause a corresponding change in one or more host vehicle motioncontrol systems, if the at least one processing device determines thatthe driver input would not result in the host vehicle navigating withinthe proximity buffer relative to the at least one obstacle. For example,the processing device may forego displacing the human driver if theprocessing device determines that the driver input would not cause thehost vehicle to come within a proximity buffer relative to any obstacle(e.g., target vehicle or VRU). Several figures disclosed herein depictconditions where the safety system would not displace the driver,including FIG. 53A.

The one or more host vehicle motion control systems may be any systemsconsistent with this disclosure. For example, the one or more motioncontrol systems may include throttling system 220, braking system 230,and/or steering system 240. In some embodiments, the one or more hostvehicle control systems may include at least one steering actuator tocontrol a heading of the host vehicle, a braking actuator to causeapplication of a host vehicle braking device, or an accelerationactuator to cause application of a host vehicle throttle. For example,throttling system 220 may include one or more acceleration actuators,braking system 230 may include one or more braking actuators, andsteering system 240 may include one or more steering actuators.

Process 5500 may include a step 5512 for displacing the human if thedriver input would cause the host vehicle to come within a proximitybuffer relative to an object. Consistent with this disclosure, the atleast one processing device may be programmed to prevent the driverinput from causing the corresponding change in the one or more hostvehicle motion control systems, if the at least one processing devicedetermines that the driver input would not result in the host vehiclenavigating within the proximity buffer relative to the at least oneobstacle. Any of the plurality of examples of unsafe conditionsdisclosed herein may be the basis for the safety system to displace thehuman driver. For example, if the driver input would cause the hostvehicle to conic within a distance of an object that is less than theRSS safe distance (or CRSS safe distance, depending on which model is inuse) the safety system may determine that the driver input is unsafe andmay displace the driver and take over control.

Consistent with this disclosure, preventing the driver input fromcausing a corresponding change in the host vehicle may includepreventing the driver input. In some embodiments, to prevent the driverinput from causing the corresponding change in the one of more hostvehicles motion control systems, the at least one processing device maybe configured to prevent motion of at least one of the throttle control,the brake control, or the steering control under certain conditions, orto prevent further motion in response to a detected driver input. Forexample, if the driver input is an acceleration caused by depression ofan acceleration pedal, the safety system may prevent the acceleration bylocking the acceleration pedal such that it cannot be depressed.Similarly, if the driver input is a clockwise rotation of a steeringwheel, the safety system may prevent the rotation by locking thesteering wheel such that it cannot be turned or that it may only beturned in a direction that corresponds with safe conditions (e.g., lockthe steering wheel from rotating clockwise, but allow acounter-clockwise rotation), In some embodiments, to prevent the driverfrom causing the corresponding change in the one or more host vehiclemotion control systems, the at least one processing device may beconfigured to disable operability of at least one of the throttlecontrol, the brake control, or the steering control. For example, if thedriver input is a depression of a brake pedal, the safety system mayprevent the input by decoupling (e.g., electronically or mechanically)the brake pedal from the rest of the braking system, such thatdepression of the brake pedal has no effect. Similarly, if the diverinput is a rotation of a steering wheel, the safety system may preventthe input by decoupling the steering wheel such that rotation of thesteering wheel (in at least the direction that would cause the unsafeconditions) has no effect. In some embodiments, prevention of the driverinput from causing the corresponding change in the one or more hostvehicle motion control systems may include at least one of preventingdriver input to the steering wheel from resulting in a correspondingresponse by the at least one steering actuator, preventing driver inputto the brake pedal from resulting in a corresponding response by thebraking actuator, or preventing driver input to the accelerator pedalfrom resulting in a corresponding response by the acceleration actuator.For example, if the driver input is a depression of an accelerationpedal, rather than locking the pedal or decoupling the pedal, the safetysystem may allow the driver to provide the input, but prevent the inputfrom having an effect, for example, by intercepting an electrical signalfrom the acceleration pedal before it reaches the acceleration actuator.In any embodiment, the prevention of the driver input may last for aperiod corresponding with the unsafe conditions. For example, the safetysystem may unlock the acceleration pedal when the processing devicedetermines that an acceleration of the host vehicle will not cause thehost vehicle to come within a distance of an object that is less thanthe distance of the proximity buffer.

Consistent with this disclosure, preventing the driver input fromcausing a corresponding change in the host vehicle may includeinhibiting the driver input. In some embodiments, to prevent the driverinput from causing the corresponding change in the one or more hostvehicle motion control systems, the at least one processing device maybe configured to prevent motion of at least one of the throttle control,the brake control, or the steering control in response to the driverinput and t(c) apply an impulse force t(c) at least one of the throttlecontrol, the brake control, or the steering control. For example, if thedriver input is a clockwise rotation of a steering wheel, the safetysystem may inhibit the rotation by locking the steering wheel such thatit cannot be rotated in a clockwise direction and by applying a forcethat causes the steering wheel to rotate in a counter clockwisedirection. In the same example, the safety system may inhibit therotation by partially locking the steering wheel such that it can berotated in a clockwise direction but the host vehicle does not respondfully to the clockwise rotation and the safety system may apply a forceto the steering wheel in the counter-clockwise direction. In someembodiments, the at least one processing device may be configured toprevent motion of at least one of the throttle control, the brakecontrol, or the steering control and to continue application of theimpulse force to at least one of the throttle control, the brakecontrol, or the steering control until driver input is received thatwould not result in the host vehicle navigating within a proximitybuffer relative to the at least one obstacle. For example, continuingthe above example, the safety system may continue inhibiting therotation of the steering wheel in the clockwise direction until thehuman driver rotates the steering wheel in a counter-clock wisedirection at a magnitude that is sufficient to cause the host vehicle toavoid an unsafe condition or return to a safe condition (e.g., wherethere are no obstacles within the proximity buffer). As another example,if the driver input is a depression of an acceleration pedal, the safetysystem may inhibit the input by supplying a force to the accelerationpedal that is opposite of the depression and may continue supplying theforce until the driver stops depressing the acceleration pedal or beginsdepressing the brake pedal. In any embodiment, the inhibition may lastuntil the host vehicle is in a safe position where there are noobstacles within the proximity buffer and there is no driver input thatwould cause the host vehicle to come within a distance of an obstaclethat is less than the proximity buffer.

Consistent with this disclosure, preventing the driver input fromcausing a corresponding change in the host vehicle may include or may beassociated with a takeover of control from the human driver. In someembodiments, the at least one processing device may be configured tocontrol navigation of the host vehicle autonomously during intervals inwhich the at least one processing device prevents the driver input fromcausing the corresponding change in the one or more host vehicle motioncontrol systems. For example, if the driver input is a clockwiserotation of a steering wheel, the safety system may prevent or inhibitthe input, as described above, and take control of steering system 240such that the driver input has no effect and the processing device is incontrol of the steering of the host vehicle. In some embodiments, if anydriver input would cause an unsafe condition, the safety system mayfully displace the human driver such that the processing device hasfully autonomous control over the host vehicle, rather than just controlof the system corresponding with the unsafe driver input. For example,if the unsafe driver input is a depression of the acceleration pedal,the A safety DAS system may take control of the acceleration system, thebraking system, and the steering system such that the processing devicemay fully navigate the host vehicle. The safety system, and theprocessing device therein, may autonomously navigate the host vehicleaccording to any embodiment of this disclosure. In some embodiments, theat least one processing device may be configured to return navigationalcontrol of the host vehicle to a driver after driver input is receivedthat would not result in the host vehicle navigating within a proximitybuffer relative to the at least one obstacle. For example, during theperiod where the safety system is autonomously navigating the hostvehicle, if the driver attempts to provide an input that would not causean unsafe condition, the safety system may terminate the autonomousnavigation and allow the human driver to take over control of the hostvehicle.

Consistent with this disclosure, the at least one processing device maybe programmed to alert a human driver. In some embodiments, the at leastone processing device may alert the driver if the processing devicedetermines that a driver input would result in an unsafe condition. Thealert may be any alert consistent with this disclosure. For example, thevehicle may include a speaker system and the safety system may providean audible alert over the speaker system. As another example, thevehicle may include one or more displays (e.g., a screen in the dash orentertainment system) and the safety system may provide a visual alerton the one or more displays. As another example, the vehicle may have aheads-up display or augmented reality display (e.g., on the frontwindshield of the vehicle) and the safety system may provide an alert onthe heads-up display or the augmented reality display. The display mayinclude, for example, an indication of which driver input would causethe unsafe condition, an indication of an input that would a safecondition, an indication that the safety system is displacing thedriver, or the like.

Consistent with this disclosure, the at least one processing device maybe programmed to collect and transmit data relating to instances whenthe safety system displaced the human driver. The data may include, forexample, information relating to the driver input that was determinedunsafe; the time, location, and duration of the displacement; the typeof displacement (e.g., prevention, inhibition, or take-over); theoutcome of the takeover (e.g., a collision has been avoided); and anyother information relating to the displacement. The data may betransmitted to one or more systems or devices. For example, the data maybe transmitted to a device associated with the driver for use ininforming the driver of avoided accidents, his or her driving abilities,or the like. As another example, the information may be transmitted toone or more systems for use in research relating to autonomous vehicles,road safety, human driving habits, or the like.

Consistent with this disclosure, the autonomous system for selectivelydisplacing human driver control of a host vehicle may include a systemoverride control for disabling the autonomous system for selectivelydisplacing human driver control. The system override control may bedifferent from the throttle control, the brake control, and the steeringcontrol. For example, having the system override control be differentfrom the brake control, throttle control, and steering control requiresthat the driver provide an input to the override control that isdifferent from a navigational input. In some embodiments, the systemoverride control may be a handle, button, lever, or other physicaldevice capable of receiving an input from a driver. For example, theoverride control may be a lever and the input that disables theautonomous system may be a pull or other displacement of the lever. Insome embodiments, the system override control may be an audible phrase,a visual gesture, or other type of input that may be detected by one ormore microphone and/or image capture device systems. For example, thesystem override control may include a hand gesture. The system overridecontrol may be any other means for deactivating or disengaging thesystem, as described above.

Consistent with this disclosure, the at least one processing device maybe configured to track when the autonomous system for selectivelydisplacing human driver control has been disabled through operation ofthe system override control. For example, the processing device maystore date relating to the time and location at which the human driveractivated the system override control and information relating to theduration that they system was disabled, including, for example, visualinformation (e.g., an image or video clip) relating to the disablementthat is show on a display or instrument panel in the vehicle. In someembodiments, if the vehicle is involved in a collision, the processingdevice may be programmed to report whether the safety system wasdisabled prior to the collision. In some embodiments, the processingdevice may be programmed to monitor the driver input even if the systemis disabled. For example, when disabled, the processing device may beconfigured to perform process 5500, except for step 5512. In thisexample, the processing device may collect and store data relating towhether the human driver caused unsafe conditions where the host vehiclewas within the proximity buffer relative to an object and otherinformation relating to navigation of the vehicle. The information maybe used to determine liability if there is a collision. For example, ifthe processing device determines that the AD safety AS system wasdisabled when a collision occurred between the host vehicle and a targetvehicle, then either the human driver of the host vehicle or the driverof the target vehicle may be liable. Similarly, if the safety system wasdisabled and the processing device determines that the human driverprovided an input that would have been displaced if the safety systemwas not disabled, then the human driver of the host vehicle may beliable.

The examples and embodiments discussed above are exemplary only and arenot limiting of the scope of the autonomous system for selectivelydisplacing human driver control. One of ordinary skill in the art havingthe benefit of this disclosure may understand how to modify theautonomous system in any manner consistent with this disclosure.

Path Prediction to Compensate for Control Delay

The autonomous navigation systems disclosed herein may determine one ormore navigational actions of a host vehicle and may implement thenavigational action. As described above, the navigational actions may bebased on one or more navigational policies, navigational goals, or thelike. The navigation systems may include one or more sensors thatprovide outputs used for determining the navigational responses of thehost vehicle. For example, the system may include a plurality of imagecapture devices configured to capture images of an environment of a hostvehicle and at least one processor configured to analyze the images anddetermine a navigational response. However, there may be a period ofdelay between the time when the image (or other output from a sensor) iscaptured and the time when a navigational response is implemented tocause a maneuver in the host vehicle. In some cases, additional delaymay exist between the time when the navigational response is implementedand the desired effect takes place, e.g., the steering Wheel is turned,and the wheel turn in response. Although the delay period may be veryshort, the vehicle in most cases continues to move during the delayperiod. As a result the sensor outputs on which a particularnavigational decision may be out-of-date, as they may be based on a pastmotion condition of the host vehicle, rather than on an actual motioncondition at a time closer to or equal to a time at which vehicleactuators cause a change in vehicle state in response to implementationof a planned navigational action. As a result, the host vehicle mayexhibit “sine wave” driving, where the vehicle may make oscillatingcorrections (e.g., brake, accelerator, brake, accelerator, etc.) due toimplementation of navigational decisions based on sensor information notrepresentative of actual conditions at the time of actuator response. Assuch, a system for predicting the motion of the vehicle after vehiclesensor measurements are made and before or simultaneous with anactuation time is disclosed. The disclosed system may avoid non-smooth,oscillating corrections that may result if no correction is made toaccount for changing vehicle motion during the sensor measurement,driving decision, and navigational action implementation times, amongothers.

The problem of controlling the speed of a vehicle may be formalized asfollows. A velocity command signal v_(cmd)(t) may be a goal velocity fora host vehicle. A navigation system may adjust the throttle and brakingcontrols such that the actual speed of the vehicle, denoted v(t), willbe as close to possible to v_(cmd)(t). Let p(t)∈[−1, 1] be the positionof a pedal where −1 corresponds with full brake, 1 corresponds with fullthrottle, and 0 means no brake and no throttle. Moving the pedal maychange the velocity of the vehicle, and the goal of the controller maybe to move the pedals such that the error signal, e(t)=v_(cmd)(t)−v(t),will be small in absolute value. In the standard notation, v_(cmd)(t) isthe desired setpoint, v(t) is the process variable, and p(t) is thecontrol variable.

A controller may run in discrete time, where the position of the pedalis moved every Δ seconds. The controller may be based on the followingsimple equations: for every t=kΔ, where k is a natural number,

${{\overset{\sim}{e}(t)}:={{( {1 - \beta} ){\overset{\sim}{e}( {t - \Delta} )}} + {\beta{e(t)}}}}{{u(t)}:={K_{p}( {{e(t)} + {K_{m}( {{e(t)} - {\overset{\_}{e}(t)}} )}} )}}{{p_{e}(t)}:={{p_{e}( {t - \Delta} )} + {{u(t)} \cdot \Delta}}}{{p(t)}:={{p_{g}( {{v_{cmd}(t)},\frac{{v_{cmd}(t)} - {v_{cmd}( {t - \Delta} )}}{\Delta}} )} + {p_{e}(t)}}}$

where p_(e) is an error correction function for the position of thepedal; p_(g)(v,a) is a “guess” function, possibly constant, of theposition of the pedal as a function of the current speed andacceleration commands (the guess function is elaborated upon below, notethat there is no dependence on feedback of v or a, so p_(g) works in acomplete “open-loop” manner); ē is a signal that gives a discountedaverage of past errors (and initialized to ē(0)=0). Observe that:

${\overset{\_}{e}( {k\Delta} )} = {{{( {1 - \beta} ){\overset{\_}{e}( {( {k - 1} )\Delta} )}} + {\beta{e( {k\Delta} )}}} = {{{( {1 - \beta} )\lbrack {{( {1 - \beta} ){\overset{\_}{e}( {( {k - 2} )\Delta} )}} + {\beta{e( {( {k - 1} )\Delta} )}}} \rbrack} + {\beta{e( {k\Delta} )}}} = {\beta{\sum\limits_{i = 0}^{k}{( {1 - \beta} )^{i}{e( {( {k - i} )\Delta} )}}}}}}$

For simplicity, the above representations do not include aspects relatedto saturation (clipping the errors, the pedal position, the change ofthe pedal). One of ordinary skill in the art having the benefit of thisdisclosure may understand that saturation may be included in the aboveformulas.

The guess function p_(g)(v,a) may be considered next. For example, avehicle may be driven while recording the speed and position of thepedals as a function of time. The derivative of the speed may be takenas the actual acceleration (even though it may be noisy), and try to fita function that gives the acceleration as a function of p(t) and v(t).Inverting this function provides the guess function p_(g)(v,a).

The guess function may provide an advantage as it has no delay. If mostof the information regarding the correct position of the pedal is in thedesired acceleration and current speed, then the guess function mayprovide an estimation of the correct pedal position. The role of thecontroller is to lose the error due to additional variables (e.g., thepressure of the tires, the heat of the engine, the tail wind, etc.) byusing p_(e).

Most of the information depends upon v and a because the main forcesacting on the vehicle are: Friction, which depends linearly on v; Lag(air resistance), which depends quadratically Gravity, which changeswith elevation in the form 9.8 sin(θ); Brake friction, which dependsupon the position of the brake pedal; and Engine, which depends upon theposition of the throttle pedal.

There may be several advantages of the guess function. First, theinitial guess (in most cases) will be very close to the optimal positionof the pedal, hence a negligible delay will result for an accelerationwhich is very close to the desired one. Second, the problem of learningthe initial guess function is an offline problem (collecting examplesfrom a human/autonomous driver and fitting a function to it). This maybe readily adapted to another vehicle, and even adapted on the fly withan existing car (the number of parameters to fit (in our choice offitting using a low degree polynomial) is much smaller than the numberof examples we can collect, so there is no fear of overfitting). Third,empirically, the discounted integrator may provide a “no steady stateerror” property of an integrator, while having a much smaller delaybecause of the discounting that quickly forgets past errors. Moreover,in some embodiments, even the existing small delay may only be on thepart of the controller which is closing the steady state error.

In some embodiments, the guess function may receive no feedback, andrather, depend on the comments. In some embodiments, this may make thep_(e) term the only controller in a navigation system using the guessfunction. Analyzing p_(e) separately:

$\begin{matrix}{{p_{e}( {k\Delta} )} = {\sum\limits_{j = 0}^{k}{\Delta{v( {j\Delta} )}}}} \\{= {\Delta K_{p}{\sum\limits_{j = 0}^{k}\lbrack {{( {1 + K_{m}} ){e( {j\Delta} )}} - {K_{m}{\overset{\_}{e}( {j\Delta} )}}} \rbrack}}} \\{= {\Delta K_{p}{\sum\limits_{j = 0}^{k}\lbrack {{( {1 + K_{m}} ){e( {j\Delta} )}} - {K_{m}\beta{\sum\limits_{i = 0}^{j}{( {1 - \beta} )^{i}{e( {( {j - i} )\Delta} )}}}}} \rbrack}}} \\{= {\Delta{K_{p}( {{\sum\limits_{j = 0}^{k}{( {1 + K_{m}} ){e( {j\Delta} )}}} - {K_{m}\beta{\sum\limits_{j = 0}^{k}{\sum\limits_{i = 0}^{j}{( {1 - \beta} )^{i}{e( {( {j - i} )\Delta} )}}}}}} )}}} \\{= {\Delta{K_{p}( {{\sum\limits_{j = 0}^{k}{( {1 + K_{m}} ){e( {j\Delta} )}}} - {K_{m}\beta{\sum\limits_{r = 0}^{k}{{e( {r\Delta} )}{\sum\limits_{j = r}^{k}( {1 - \beta} )^{j - r}}}}}} )}}} \\{= {\Delta K_{p}{\sum\limits_{r = 0}^{k}{( {( {1 + K_{m}} ) - {K_{m}\beta{\sum\limits_{j = r}^{k}( {1 - \beta} )^{j - r}}}} ){e( {r\Delta} )}}}}} \\{= {\Delta K_{p}{\sum\limits_{r = 0}^{k}{( {( {1 + K_{m}} ) - {K_{m}\beta{\sum\limits_{j = 0}^{k - r}( {1 - \beta} )^{j}}}} ){e( {r\Delta} )}}}}} \\{= {\Delta K_{p}{\sum\limits_{r = 0}^{k}{( {( {1 + K_{m}} ) - {K_{m}\beta\frac{1 - ( {1 - \beta} )^{k - r}}{\beta}}} ){e( {r\Delta} )}}}}} \\{= {\Delta K_{p}{\sum\limits_{r = 0}^{k}{( {( {1 + K_{m}} ) - {K_{m}( {1 - ( {1 - \beta} )^{k - r}} )}} ){e( {r\Delta} )}}}}} \\{= {\Delta K_{p}{\sum\limits_{r = 0}^{k}{( {1 + {K_{m}( {1 - \beta} )}^{k - r}} ){e( {r\Delta} )}}}}}\end{matrix}$

In some embodiments, the controller operating according to the equationsherein may depend on an integrator with coefficients that decay withtime. It should be noted that the non-decaying term in the coefficientmay be relative small as Km>>1. As discussed, this type of integratormay have a “no steady state error” property while suffering less delayfrom past errors because of the discounting effect. This may also beinterpreted as something between the P and I terms in a regular PIcontroller: e.g., no discounting at all gives a classical I-term, whileharsh discounting gives a classical P-term. As such, the controller mayprovide a distinct advantage over existing PI controllers,

FIG. 56 depicts an overview of a process 5600 that may be performed by anavigation system. The following discussion illustrates how a controlleraccount for a processing delay. Process 5600 may include a sensing andoutput stage 5602 in which the navigation system may collect data fromone or more sensors and analyze the data to generate one or moreoutputs. For example, at sensing and output stage 5602 an image capturedevice 122 may capture one or more images and provide those images to atleast one processing device programmed to analyze the images to detectobstacles in the environment of a host vehicle. Sensing and output stage5602 may end with an output related to the one or more sensors, such asa determination that a target vehicle is in front of the host vehicle.Sensing and output stage 5602 may also include measurements by anysensors associated with a host vehicle (e.g., UPS, accelerometers,speedometers, tire pressure indicators, RADAR, LIDAR, etc.). Process5600 may include a navigational command determination stage 5604 inwhich the navigation system may include at least one processing deviceprogrammed to use the output from sensing and output stage 5602 todetermine one or more navigational commands for the host vehicle. Forexample, at least one processing device may determine a navigationalcommand using, for example, one or more navigational policies along withthe output from the sensor outputs. Navigational command determinationstage 5604 may end with a navigational command being transmitted to oneor more motion control systems (e.g., a throttle control system, abraking control system, a steering control system, etc.). Process 5600may include a navigational response stage 5606 for causing the vehicleto perform a navigational maneuver consistent with the navigationalcommand(s) from navigational command stage 5604. For example,navigational response stage 5606 may include activating a throttleactuator in response to a navigational command from navigational commanddetermination stage 5604.

In this example, t(0) may represent an instant where a sensormeasurement is made (e.g., the image capture device 122 captures a firstimage); t(1) may represent an instant where a sensor output istransmitted to one or more processing devices; t(2) may represent aninstant the sensor output is received by the processor programmed todetermine a navigational command based on one or more received sensoroutputs; t(3) may represent an instant that the processor transmits adetermined navigational command to one or more motion control systems;t(4) may represent an instant that the one or more motion controlsystems receive the transmitted navigational command; and t(5) mayrepresent an instant that the navigational command is given effect(e.g., an actuator causes a throttle, brake, or steering response).Consistent with this disclosure, there may be a delay between any of theinstances. For example, the total delay of process 5600 may be thedifference between t(5) and t(0), which may be a range from, forexample, one millisecond to several hundred milliseconds. For example,in some configurations of process 5600, the delay may be 150milliseconds. The accumulated delay may include processing times forcollecting, packaging, and transmitting a sensor output at stage 5602,for applying a driving policy, etc., to one or more received sensoroutputs in order to generate a planned navigational action command atstage 5604, and for transmitting the or otherwise effecting the receivednavigational command at stage 5606.

During the accumulated delay or any part of the total delay, the hostvehicle may continue navigating at the same or different speed,acceleration, and or path at which it was traveling at data acquisitiontime t(0). For example, if the brakes are being applied at the time of asensor measurement, the vehicle speed may be lower than at sensormeasurement time by the time a navigational command is implemented.Similarly, if an accelerator is being applied at the time of a sensormeasurement, the vehicle speed may be higher than at sensor measurementtime by the time a navigational command is implemented. When thenavigational command is given effect at actuation time t(5), the vehiclemay have traveled a significant distance and/or may have a differentspeed, acceleration, or path than was the basis for the navigationalcommand. As such, the navigational command may cause a navigationalresponse at actuation time t(5) that is not based on actual motionconditions of the vehicle at the time the navigational command is putinto effect by the motion control system.

FIGS. 57A-57C illustrate conditions in which a prediction of vehiclepath during a time between sensor measurements and actuation may beuseful. FIGS. 57A-57C each depict a host vehicle 5702 and a targetvehicle 5706 on roadway 5700 at an data acquisition time t(0), Dataacquisition time t(0) may be the instant in which one or more sensors onhost vehicle 5702 captures information relating to target vehicle 5706.FIGS. 57 a and 57C also depict host vehicle 5702′ and target vehicle5706′ at a delay time t(5). Delay time t(5) may be the instant when thehost vehicle performs a navigational maneuver or otherwise implements anavigational command, as discussed in relation to FIG. 56 .

FIG. 57A depicts host vehicle 5702 at initial time t(0) and the samehost vehicle 5702′ at delay time t(5). As depicted, there is a slightpositional difference between host vehicle 5702 at initial time t(0) andhost vehicle 5702′ at delay time t(5). The difference in position may beattributed to the distance that host vehicle 5702 traveled during theresponse period Δt (not shown), which is the difference between delaytime t(5) and initial time t(0). Similarly, host vehicle 5706 may havetraveled a distance during response period Δt. In this example, anavigational command determined based on the position of host vehicle5702 and target vehicle 5706 at initial time t(0) may not cause an idealnavigational response at delay time t(5) because the position of hostvehicle 5702′ and target vehicle 5706′ is different at delay time t(5)than at initial time t(0).

FIG. 57B depicts an exemplary path 5704 that may correspond with adesired trajectory of host vehicle 5702. For example, the at least oneprocessor in the navigational system of host vehicle 5702 may determinethat host vehicle 5702 should pass target vehicle 5706 and may generatea navigational command consistent with path 5704. In this example, path5704 is generated based on the conditions at initial time t(0). Forexample, path 5704 may be based on the speed, acceleration, maximumbraking capability, and position of target vehicle 5706 at initial timet(0) and the speed, acceleration, position, and one or more navigationalpolicies associated with host vehicle 5702 at initial time t(0).

FIG. 57C depicts the different paths 5704, 5704′, and 5710 that hostvehicle 5702, 5702′ may travel. Path 5704 is the desired path determinedunder the conditions of initial time t(0), as shown in FIG. 57B. In thisexample, at delay time t(5), host vehicle 5702′ is in a position whereit cannot follow path 5704 because the starting point of path 5704 isbehind the front of vehicle 5702′ at delay time t(5). As such, hostvehicle 5702′ at time t(5) cannot follow path 5704 generated at timet(0). Path 5704′ may be the trajectory that vehicle 5702′ would travelif it were to perform the navigational maneuvers consistent with path5704. In other words, path 5704′ is the trajectory that would result ifhost vehicle 5702′ were to perform at delay time t(5) the navigationalcommands generated for host vehicle 5702 at initial time t(0). In thisexample, path 5704′ is much closer to target vehicle 5706′ at delay timet(5) than path 5704 would be to target vehicle 5706 at initial timet(0). In some embodiments, the distance between path 5704′ and targetvehicle 5706′ may be considered an unsafe distance (e.g., the distancemay breach a proximity buffer of host vehicle 5702′). Path 5710 may be apath for host vehicle 5702′ that was generated at initial time t(0)based on a predicted path of host vehicle 5702 and target vehicle 5706.For example, at initial time t(0), the navigational system of hostvehicle 5702 may predict a position of target vehicle 5706 at delay timet(5) (which may be the position depicted by target vehicle 5706′) andmay predict a position of host vehicle 5702 at delay time t(5) (whichmay be the position depicted by host vehicle 5702′) and may generatenavigational commands consistent with path 5710, which will beimplemented at delay time t(5). As shown by this example, path 5710based on the predicted conditions may provide a distinct safetyadvantage over path 5704′.

The examples above are illustrative only and not limiting on the scopeof the embodiments. For example, while FIGS. 57A-57C depict a predictedpath for a host vehicle passing a target vehicle, the predicted path maybe associated with any navigational maneuver of the host vehicle and mayrelate to any obstacle (e.g., a VRU, a plurality of host vehicles, aroad characteristic, etc.). As an example, a predicted path may begenerated for a host vehicle entering a turn in a roadway. Any othernavigational maneuver may benefit from the predicted path analysisand/or the guess function as described above.

In some embodiments, the delayed response may cause an over-correctionor unnecessary navigational response by the host vehicle. For example,if a target vehicle in front of a host vehicle is traveling with a lowvelocity but with a high acceleration, an image captured at time 40) maybe used to determine that the host vehicle may need to stop or swerve toavoid colliding with the target vehicle. However, at time t(5), thetarget vehicle may have traveled a significant distance due to its highacceleration and the host vehicle may avoid colliding with the targetvehicle by, for example, coasting or braking at a sub-maximal brakingrate. In this example, if the host vehicle is equipped with a systemprogrammed to determine a predicted path based on conditions predictedfor time t(5) rather than based on the present conditions at time 40),the host vehicle may more accurately and comfortably respond to thedetected target vehicle. In some embodiments, the delayed response maycause the host vehicle to perform an inadequate navigational response,which may cause the host vehicle to enter unsafe conditions. Forexample, if a target vehicle is traveling at a safe distance butdecelerating quickly and a host vehicle is accelerating towards thetarget vehicle, the distance determined based on sensed conditions attime 40) may be significantly longer than an actual distance at timet(5) when the host vehicle implements a navigational command determinedbased on the conditions at time 40). As such, the host vehicle may notbrake, swerve, or otherwise avoid unsafe conditions as programmed.

Consistent with this disclosure, a navigation system for navigating anautonomous host vehicle according to at least one navigational goal ofthe host vehicle is disclosed. The navigation system may be anynavigation consistent with this disclosure, including but not limited tothe disclosed Vision Zero safety system. The system may be within or incommunication with the host vehicle. The system may include one or moresensors configured to collect data relating to an environment of thehost vehicle. For example, the navigation system may include one or moreimage capture devices, LIDAR systems, RADAR systems, accelerometers, orthe like. The system may include at least one processor programmed toperform one or more methods, processes, operations, or functionsconsistent with this disclosure. The at least one processor may be, forexample, processing device 110 or any other processing device consistentwith this disclosure.

FIG. 58 is a flowchart depicting an exemplary process 5800 fornavigating an autonomous host vehicle according to at least onenavigational goal of the host vehicle, Consistent with this disclosure,the at least on processor may be programmed to perform all or part ofprocess 5800. Process 5800 is exemplary only and one of ordinary skillin the art having the benefit of this disclosure may understand thatprocess 5800 may include additional steps, may exclude one or moresteps, or may be otherwise modified in ways consistent with thisdisclosure.

Process 5800 may include a step 5802 for receiving a sensor outputindicative of motion of a host vehicle. Consistent with this disclosure,the at least one processor may be programmed to receive a sensor outputindicative of at least one aspect of motion of the host vehicle relativeto an environment of the host vehicle. The output may be received fromone or more sensors. The one or more sensors may include any sensorsdisclosed herein including, for example, an image capture device, asensing system, an accelerometer, a GPS unit, or the like. For example,the one or more sensors may include a speed sensor, an accelerometer, acamera, a LIDAR system, or a RADAR system. The output may include orconvey any information relating to the host vehicle, the environment ofthe host vehicle, an obstacle in the environment of the host vehicle,and so forth. For example, the output may include a current speed and/oracceleration of the host vehicle, a heading direction of the hostvehicle, a position of the host vehicle, etc. As another example, theoutput may include an identification of a detected target vehicle, aposition of the target vehicle, a speed of the target vehicle, and anassumed braking capability of the target vehicle, as detected based onanalysis of one or more images, LIDAR, or RADAR, for example. The outputmay be determined according to any method, process, function, oroperation consistent with this disclosure.

In some embodiments, the sensor output may be generated at a first timethat is later than a data acquisition time, when a measurement or dataacquisition on which the sensor output is based is acquired, and earlierthan a second time at which the sensor output is received by the atleast one processor. In some embodiments, the data acquisition time maybe an instant when the one or more sensors made a measurement or dataacquisition and the first time may be an instant when an output based onthe measurement or data is ready to be output. For example, referring toFIG. 56 , the output may be generated at first time t(1) and be based ondata acquired at data acquisition time t(0). In some embodiments, thetime between the data acquisition time and the first time may be severalmilliseconds. For example, the time between first time t(1) and dataacquisition time t(0) may be more than 2 milliseconds, more than 10milliseconds, a range of 5 to 50 milliseconds, fewer than 100milliseconds, or any other time period. In some embodiments, the secondtime may be an instant when a controller receives the sensor output. Forexample, the second time may be time t(2). The controller may include,for example, the controller described above in relation to the guessfunction, or the at least one processor programmed to perform the guessfunction.

Process 5800 may include a step 5804 for generating a prediction of atleast one aspect of the host vehicle motion. Consistent with thisdisclosure, the at least one processor may be programmed to generate,for a motion prediction time, a prediction of at least one aspect ofhost vehicle motion. The at least one processor may determine or projecta future time corresponding with motion prediction time. The motionprediction time may be a future time at which the host vehicle mayperform a navigational response. In some embodiments, the motionprediction time may substantially correspond with an actuation time. Forexample, the motion prediction time may be a prediction of whenactuation time t(5) will occur, at which one or more actuators mayimplement a navigational command. The motion prediction time, however,can also correspond to any time after t(0) and before t(5). For example,a motion of a host vehicle may be predicted for any of t(1), t(2), t(3),t(4) or at other times prior to t(5).

In some embodiments, the motion prediction time may substantiallycorrespond with the time at which a controller receives the sensoroutput (e.g., time t(2)). In other cases, the motion prediction time mayaccount for a time a processor requires to operate on a sensor output.For example, if a processor requires approximately 100 milliseconds toperform a function such as detection of a target vehicle, determinationof an appropriate navigational action in response to one or more sensedconditions, etc., the at least one processor may assume that the motionprediction time is 100 milliseconds after the second time, t(2). In someembodiments, the motion prediction time may substantially correspondwith a third time, at which an actuation system receives a navigationalcommand determined based on the sensor output (e.g., at time t(4)). Themotion prediction time may also correspond to a time that is after thethird time (e.g., time t(4)) by a predetermined or determined amount.For example, if braking system 230 receives a navigational command attime t(4), the motion prediction time may be a time after time t(4) thatcorresponds with an average actuator response time of braking system230.

The motion prediction time may be any time period after the dataacquisition time. In some embodiments, the motion prediction time may beafter the data acquisition time and earlier than or equal to anactuation time. For example, the motion prediction time may be at least100 milliseconds after the data acquisition time. In another example,the motion prediction time may be at least 200 milliseconds after thedata acquisition time. In another example, the motion prediction timemay be 50-100 milliseconds after the data acquisition time, 75-275milliseconds after the data acquisition time, 100-250 milliseconds afterthe data acquisition time, 150-200 milliseconds after the dataacquisition time, or the like.

In some embodiments, the prediction of at least one aspect of hostvehicle motion may be based, at least in part, on the received sensoroutput, and on an estimation of how the at least one aspect of hostvehicle motion changes over a time interval between the data acquisitiontime and the motion prediction time i.e., a time at which a vehiclemotion based on earlier acquired sensor output(s) is predicted). Forexample, if the at least one aspect of the host vehicle motion is anacceleration of the host vehicle, the prediction may include a distancetraveled by the host vehicle if it traveled at the detected accelerationduring the time between the motion prediction time. The prediction maybe based on the received sensor output and any other informationconsistent with this disclosure. For example, the prediction may bebased on an output from an image sensor (such as a detection of a targetvehicle) and a previously determined road characteristic, weathercondition, or other factor that may affect a future condition relativeto the host vehicle. In some embodiments, the prediction may include anestimate of the at least one aspect of the host vehicle motion at alater time (e.g., at time t(5)). As a result, a navigational decisionmay be based on an estimation of vehicle motion that may be closer toactual motion values corresponding to the acquired sensor outputs sensedat the initial time (e.g., at time t(0)).

In some embodiments, the prediction of at least one aspect of hostvehicle motion may include a prediction of at least one of a speed or anacceleration of the host vehicle at the motion prediction time. The atleast one aspect may include, for example, a speed, acceleration,position, yaw, or other aspect of the host vehicle motion. For example,if the acceleration and/or speed of the host vehicle is determined attime t(1) based on sensor output(s) acquired at data acquisition timet(0), the at least one processor may determine a predicted future speedand future acceleration of the host vehicle at time t(5) or at anothermotion prediction time. For example, the at least one processor mayassume that the host vehicle accelerated from time t(0) to time t(5) oranother motion prediction time at the same acceleration rate determinedat time t(0) and, therefore, may determine that the host vehicle has aspeed at time t(5) that is greater than that at time t(0). Accordingly,the at least one processor may predict a speed and/or acceleration atthe motion prediction time in order to determine a navigational actionappropriate to the estimated speed at time t(5) or other motionprediction time.

In some embodiments, the prediction of at least one aspect of hostvehicle motion may include a prediction of a path of the host vehicle atthe motion prediction time. For example, if the host vehicle istraveling on a path at time t(0), the at least one processor may use theinformation from the one or more sensors to predict a path on which thehost vehicle will be traveling at time t(5) (e.g., a changed headingdirection, etc.). As an example, if the sensor output indicates that thehost vehicle is traveling in a straight, forward path at a constantspeed, the at least one processor may predict that the host vehicle willbe on the same straight path at time t(5) but may be further along thepath. As another example, if the sensor output indicates that the hostvehicle is traveling a curvilinear path associated with a certainrotation of a steering wheel, the at least one processor may predictthat the host vehicle may be on a path associated with the same rotationof the steering wheel or a path associated with an increased rotation ofthe steering wheel. In such cases, the predicted path may be based on adetected rate of change in a steering controller or may be based on adetected yaw rate, a detected centripetal acceleration, a detection ofroad curvature ahead of the vehicle, etc. In some embodiments, theprediction of the path of the host vehicle at motion prediction time mayinclude a target heading direction for the host vehicle. For example,the target heading may include a direction in which the host vehicle isto travel. As an example, if the output from the sensor indicates thatthere is an obstacle that host vehicle needs to avoid, the targetheading may be a direction in which the host vehicle needs to travel toavoid the obstacle. The target heading direction may be a directioncorresponding with the cardinal directions or may be based on apredetermined coordinate system. For example, a direction may be North,Northeast, East, Southeast, South, or the like or may be indicated by anexpected heading angle (e.g., relative to a current heading angledetermined at the time of sensor measurements). In another example, aheading direction may be expressed based on a degree on a horizontal orvertical axis through the body of the host vehicle, a yaw rate, or thelike. In some embodiments, the one or more sensors may include a camera,and the prediction of the path of the host vehicle at the motionprediction time may be based on at least one image captured by thecamera. For example, the path may include a virtual trajectory throughthe environment captured in the image and may include a representationof the path over or on the image. As another example, the prediction ofthe path may include, for example, a route between two obstaclesdetected in the images.

In some embodiments, the prediction of the path of the host vehicle atthe motion prediction time may be based on at least a determined speedfor the host vehicle and a target trajectory for the host vehicleincluded in a map of a road segment on which the host vehicle travels.For example, the predicted path may be generated according to a semantichigh-definition mapping technology, such as REM, discussed above. As anexample, the road segment on which the host vehicle is traveling may beassociated with a plurality of trajectories which may be used tonavigate autonomous vehicles on the road segment and the predicted pathmay include a position on one of the target trajectories associated withthe road segment. As another example, if the host vehicle is determinedto be traveling according to a predetermined target trajectory, thepredicted path at the motion prediction time may include a position,speed, and/or acceleration along the same target trajectory. In someembodiments, the target trajectory may include a predeterminedthree-dimensional spline representative of a preferred path along atleast one lane of the road segment. For example, the three-dimensionalspline may include a plurality of landmarks, road features, and otherobjects that define the target trajectory on the road segment. In thisexample, the predicted path may include a prediction of which landmarks,road features, or other objects may be in the proximity of the hostvehicle at the motion prediction time. For example, if the host vehicleis determined to be on a target trajectory based on the host vehicle'sposition between a first and second landmark, the predicted path mayinclude a position on the target trajectory that is between thelandmarks. If the host vehicle is navigating according to a targettrajectory in a REM map, then localization along the target trajectoryat a certain point in time (e.g., at time t(0)) may be used to predict apath at a later time. For example, if the speed of the host vehicle isknown and the host vehicle's position relative to a REM targettrajectory is known at time t(0), then at a later time (e.g., at timet(5), which may be determined based on known processing time delays,then the position of the host vehicle may be estimated relative to theREM target trajectory. And, if the position on the REM target trajectoryis known, the heading direction at that location may be determined fromthe map (as the heading direction may correspond to a direction the hostvehicle will travel at time t(0) in order to continue following the REMtarget trajectory).

In some embodiments, the prediction of at least one aspect of hostvehicle motion (e.g., speed) may be based on at least one of adetermined brake pedal position, a determined throttle position,determined air resistance opposing host vehicle motion, friction, orgrade of a road segment on which the host vehicle travels. For example,the prediction may be based on the pedal position as defined in theguess function and other formulas disclosed above. The guess functionmay be determined empirically by observing resulting vehicle speeds, forexample, in response to brake pedal and/or throttle pedal position. Forexample, a vehicle may slow according to a certain deceleration profilecorresponding to a certain brake pedal position. Similarly, a vehiclemay accelerate according to a certain acceleration profile correspondingto a certain throttle pedal position.

As another example, if the output of the sensors includes a speed and/oracceleration of the host vehicle, the at least one processor may predicta future speed and/or acceleration using the initial speed and/oracceleration and the resistive forces like friction or air resistance(or gravity based on road grade). In some embodiments, the at least oneaspect of host vehicle motion may be determined by determining anoverall force on the host vehicle and modifying the current speed and/oracceleration of the host vehicle based on the overall force. In thisexample, the overall force may include a sum of the assistive forces(e.g., throttle, acceleration, gravity when traveling down-hill, etc.)and the resistive forces (e.g., wind-resistance, friction, gravity whentraveling up-hill, etc.) and a current speed of the host vehicle may beused to predict a future speed using the overall force.

In some embodiments, the prediction of at least one aspect of hostvehicle motion may be based on a predetermined function associated withthe host vehicle. The predetermined function may enable prediction offuture speed and acceleration of the host vehicle based on a determinedcurrent speed of the host vehicle and a determined brake pedal positionof a determined throttle position for the host vehicle. For example, theprediction of at least one aspect of host vehicle motion may includeusing the guess function to predict a future speed, acceleration, and/orposition of the host vehicle. For example, as described above, theposition of the brake and throttle pedal may be defined by p(t)∈[−1, 1]where −1 corresponds with full brake, 1 corresponds with full throttle,and 0 corresponds with no brake and no throttle and the at least oneprocessor may use the guess function to predict an aspect of hostvehicle motion based on the pedal position.

In some embodiments, the prediction of at least one aspect of hostvehicle motion at the motion prediction time may account for a mismatchbetween a data acquisition rate associated with the one or more sensorsand a control rate associated with a rate that the at least oneprocessor generates a navigational command. For example, one or moresensors may acquire data at a slower rate than the at least oneprocessor may process the data to generate a navigational command basedon the data. As a particular example, one or more cameras may acquireimages at 10 Hz, but the at least one processor may generatenavigational commands based on the images at a rate of 50 Hz. As aresult, a new image on which navigational decisions may be based may beavailable only for every fifth processing event. In such cases, vehiclemotion may be predicted for those processing events (occurring at up to50 Hz) that may occur between image capture events (which occur at 10Hz).

Process 5800 may include a step 5806 for determining a plannednavigational action for the host vehicle. The planed navigational actionmay be based on, for example, the prediction of the host vehicle motionand/or a navigational goal of the host vehicle. Consistent with thisdisclosure, the at least one processor may be programmed to determine aplanned navigational action for the host vehicle based, at least inpart, on the at least one navigational goal of the host vehicle (e.g.,navigating along an intended route from point A to point B) and based onthe generated prediction of the at least one aspect of host vehiclemotion. The planned navigation action may be any navigational actiondescribed herein, including an acceleration, a deceleration, a turn, aveer, a plurality of navigational maneuvers, or the like. For example,the planned navigational action may include at least one of a speedchange or a heading change for the host vehicle. As another example, theplanned navigational action may include a desired trajectory or path forthe host vehicle to follow. For example, the navigational action may bedetermined according to any of the embodiments described herein. Incertain cases, however, the navigational actions in the presentlydisclosed embodiments may be determined based on predicted aspects ofthe host vehicle motion at times later than a sensor measurement time.For example, rather than determining a target trajectory for the hostvehicle using raw sensed conditions, the processing device may determinea target trajectory based on those sensed conditions and resultingchanges in vehicle motion predicted to occur after acquisition of thesensed conditions. Using the predicted vehicle motion may have severaladvantages over other embodiments. For example, referring to FIG. 57C,if the target trajectory is determined based on the sensed conditionsfrom time t(0), host vehicle 5702′ would travel path 5704′, which comeswithin a distance of target vehicle 5706′ that may be unsafe (e.g., maybe within a proximity buffer and/or less than an RSS or CRSS safedistance) whereas if the target trajectory is determined based on thepredicted conditions, host vehicle 5702′ would travel path 5710, whichmaintains safe conditions with respect to target vehicle 5706′.Additionally, by predicting vehicle speed at a motion prediction timelater than sensor measurement time, and closer to or equal to anactuator time, a host vehicle may drive more smoothly and with less orwithout sine wave/oscillating corrections that may be uncomfortable topassengers.

In some embodiments, the navigational goal of the host vehicle mayinclude translation from a first location to a second location. Forexample, the first location may be a starting point and the secondlocation may be a destination. In this example, the predicted aspects ofhost vehicle motion may be used to determine one or more navigationalactions consistent with the navigational goal (e.g., one or more actionsthat may cause the host vehicle to become closer to the destinationalong a selected route or target trajectory). As another example, thefirst location may be a first position on a target trajectory and thesecond location may be a second position on the target trajectory. Inthis example, the navigational action may be any navigational maneuverthat would cause the host vehicle to travel along the target trajectorytowards the second position, as discussed above in relation to the REMmaps and associated navigation. In some embodiments, the navigationalgoal of the host vehicle may include a change of lane from a currentlane occupied by the host vehicle to an adjacent lane. For example, thenavigational goal may be path 5704, as described in relation to FIG.57B. In this example, the processing device may use the predictedaspects of host vehicle motion to determine a navigational action thatcorresponds with the goal, such as by developing path 5710 for the hostvehicle to follow.

In some embodiments, the navigational goal of the host vehicle mayinclude maintaining a proximity buffer between the host vehicle and adetected target vehicle. As discussed above, the proximity buffer may bedetermined based on a detected current speed of the host vehicle, amaximum braking rate capability of the host vehicle, a determinedcurrent speed of the target vehicle, and an assumed maximum braking ratecapability of the target vehicle. The proximity buffer relative to thetarget vehicle may be further determined based on a maximum accelerationcapability of the host vehicle, such that the proximity buffer includesat least a sum of a host vehicle acceleration distance, determined as adistance over which the host vehicle will travel if accelerated at themaximum acceleration capability of the host vehicle over a reaction timeassociated with the host vehicle; a host vehicle stopping distance,determined as a distance required to reduce the current speed of thehost vehicle to zero at the maximum braking rate capability of the hostvehicle; and a target vehicle stopping distance, determined as adistance required to reduce the current speed of the target vehicle tozero at the assumed maximum braking rate capability of the targetvehicle. For example, the host vehicle may have an safety systemconfigured to maintain a proximity buffer between the host vehicle andone or more obstacles, as described above. In this embodiment, theproximity buffer may be based on an RSS safe distance. In someembodiments, the proximity buffer may be based on a CRSS safe distance,as discussed in relation to FIGS. 52A 52D. The planned navigation actionin this example may be any navigational maneuver that would maintain theproximity buffer.

Process 5800 may include a step 5808 for generating a navigationalcommand for implementing the planned navigational action. Consistentwith this disclosure, the at least one processor may be programmed togenerate a navigational command for implementing at least a portion ofthe planned navigational action. The navigational command may be anyinstruction for causing one or more maneuvers consistent with thisdisclosure. For example, the command may include instructions forcausing a braking system to apply the brake at a certain level or forcausing a throttling system to accelerate at a certain level. In someembodiments, the navigational command may include at least one of apedal command for controlling a speed of the host vehicle or a yaw ratecommand for controlling a heading direction of the host vehicle. Forexample, the navigational command may include instructions for causing athrottle pedal to be depressed by an amount corresponding with anacceleration determined for the planned navigational action. Thenavigational commands may include any other command or instructionconsistent with this disclosure. For example, the command may include asemantic or non-semantic command for causing the host vehicle to changeheading, accelerate, decelerate, change speed, coast, stop, or the like.

The examples of navigational actions, navigational goals, andnavigational commands described above are for illustration only. One ofordinary skill in the art having the benefit of this disclosure mayunderstand that any of the embodiments described herein may be modifiedto determine a planned navigational action using the predicted aspectsof host vehicle motion. For example, the embodiments discussed relationto the REM model, the RSS model, and the CRSS model and embodimentsdiscussed in relation to FIGS. 13-15 and 18 may be modified using thepredicted aspects of host vehicle motion.

Process 5800 may include a step 5810 for providing the navigationalcommand to at least one actuation system of the host vehicle. Consistentwith this disclosure, the at least one processor may be programmed toprovide the navigational command to at least one actuation system of thehost vehicle, such that the at least one actuation system receives thenavigational command at a third time that is later than the second timeand earlier or substantially the same as an actuation time at which acomponent of the at least one actuation system responds to the receivedcommand. For example, referring to FIG. 56 , the navigational commandmay be provided to an actuation system at time t(4), which is prior toor at substantially the same time as time t(5) at which the command isimplemented by one or more actuators. The actuation system may be anysystem that is configured to cause one or more responses to thenavigational command. For example, the at least one actuation system mayinclude one or more of a throttle actuation system, a braking actuationsystem, or a steering actuation system. As a particular example, thethrottle actuation system may include throttling system 220, the brakingactuation system may include braking system 230, and the steeringactuation system may include steering system 240.

As described above, the actuation system may cause a navigationalresponse at time t(5) based on motion aspects predicted for actuationtime t(5) that is more accurate, precise, and/or safe than a response atactuation time t(5) that is based directly on motion aspects sensed attime t(0). This is because the predicted motion aspects may be moresimilar to the actual conditions at actuation time t(5) than the sensedmotion aspects at time t(0). In some embodiments, the motion predictiontime may be after the data acquisition time and earlier than or equal tothe actuation time. The closer the motion prediction time is to theactual actuation time, the more accurate, precise, and safe thenavigational action may be. For example, at actuation time t(5) the oneor more actuation systems may cause a navigational action correspondingwith the planned navigational action that is based on the predictedaspects of host vehicle motion, which may correspond to execution of anavigational action that closely matches the planned navigational actionif the motion prediction time is close to the actuation time. Forexample, the motion prediction time may be substantially similar toactuation time t(5) and the predicted motion aspects associated with themotion prediction time may be substantially similar to the actual motionaspects at actuation time t(5).

The embodiments disclosed herein are exemplary and any other means forpredicting one or more aspects of host vehicle motion and for causing anavigation response based on the prediction may be consistent with thisdisclosure.

The foregoing description has been presented for purposes ofillustration. It is not exhaustive and is not limited to the preciseforms or embodiments disclosed. Modifications and adaptations will beapparent to those skilled in the art from consideration of thespecification and practice of the disclosed embodiments. Additionally,although aspects of the disclosed embodiments are described as beingstored in memory, one skilled in the art will appreciate that theseaspects can also be stored on other types of computer readable media,such as secondary storage devices, for example, hard disks or CD ROM, orother forms of RAM or ROM, USB media, DVD, Blu-ray, 4K Ultra HD Blu-ray,or other optical drive media.

Computer programs based on the written description and disclosed methodsare within the skill of an experienced developer. The various programsor program modules can be created using any of the techniques known toone skilled in the art or can be designed in connection with existingsoftware. For example, program sections or program modules can bedesigned in or by means of .Net Framework, .Net Compact Framework (andrelated languages, such as Visual Basic, C, etc.), Java, C++,Objective-C, HTML, HTML/AJAX combinations, XML, or HTML with includedJava applets.

Moreover, while illustrative embodiments have been described herein, thescope of any and all embodiments having equivalent elements,modifications, omissions, combinations (e.g., of aspects across variousembodiments), adaptations and/or alterations as would be appreciated bythose skilled in the art based on the present disclosure. Thelimitations in the claims are to be interpreted broadly based on thelanguage employed in the claims and not limited to examples described inthe present specification or during the prosecution of the application.The examples are to be construed as non-exclusive. Furthermore, thesteps of the disclosed methods may be modified in any manner, includingby reordering steps and/or inserting or deleting steps. It is intended,therefore, that the specification and examples be considered asillustrative only, with a true scope and spirit being indicated by thefollowing claims and their full scope of equivalents.

What is claimed is:
 1. An automated driving system for a host vehicle,the system comprising: an interface to obtain sensing data of anenvironment in a vicinity of the host vehicle, the sensing data capturedfrom at least one sensor device of the host vehicle; and at least oneprocessing device configured to: determine a planned navigational actionfor accomplishing a navigational goal of the host vehicle; identify,from the sensing data, a target vehicle in the environment of the hostvehicle; predict a following distance between the host vehicle and thetarget vehicle that would result if the planned navigational action wastaken; identify a defined braking capability of the host vehicle, adefined acceleration capability of the host vehicle, and a longitudinalspeed of the host vehicle; determine a host vehicle braking distancebased on an evaluation of: (i) the defined braking capability of thehost vehicle, (ii) the defined acceleration capability of the hostvehicle, and (iii) the longitudinal speed of the host vehicle, whereinthe defined braking capability of the host vehicle comprises a minimumbraking rate that is less than a maximum braking rate of the hostvehicle, wherein the minimum braking rate is identified to be applied bythe host vehicle as at least an initial braking force used to deceleratewithin the host vehicle braking distance, and wherein the minimumbraking rate is identified to be applied by the host vehicle as a lowerlimit of an amount of braking force used to decelerate throughout thehost vehicle braking distance; determine a target vehicle brakingdistance, based on an evaluation of: (i) a longitudinal speed of thetarget vehicle and (ii) a maximum braking capability of the targetvehicle; and cause the host vehicle to implement the plannednavigational action when the predicted following distance of the plannednavigational action is greater than a minimum safe longitudinaldistance, wherein the minimum safe longitudinal distance is calculatedbased on the determined host vehicle braking distance and the determinedtarget vehicle braking distance.
 2. The system of claim 1, wherein theminimum safe longitudinal distance includes an acceleration distancethat corresponds to a distance the host vehicle can travel over a timeperiod at a maximum acceleration capability of the host vehicle,starting from the identified longitudinal speed of the host vehicle. 3.The system of claim 1, wherein the minimum safe longitudinal distance isfurther calculated based on a response time associated with the hostvehicle.
 4. The system of claim 1, wherein the defined brakingcapability of the host vehicle is based on weather and road conditionsof the environment.
 5. The system of claim 1, wherein the longitudinalspeed of the target vehicle is determined from the sensing data.
 6. Thesystem of claim 1, wherein the longitudinal speed of the target vehicleis determined from output from at least one of a LIDAR system or a RADARsystem of the host vehicle.
 7. The system of claim 1, wherein theplanned navigational action causes at least one of steering, braking, oraccelerating in the host vehicle.
 8. The system of claim 1, wherein theat least one sensor device includes a camera, and wherein the sensingdata includes at least one image captured from the camera.
 9. At leastone non-transitory machine-readable storage medium comprisinginstructions stored thereupon, which when executed by a processor of anavigation system of a host vehicle, cause the processor to performoperations comprising: obtaining sensing data of an environment in avicinity of the host vehicle, the sensing data captured from at leastone sensor device of the host vehicle; determining a plannednavigational action for accomplishing a navigational goal of the hostvehicle; identifying, from the sensing data, a target vehicle in theenvironment of the host vehicle; predicting a following distance betweenthe host vehicle and the target vehicle that would result if the plannednavigational action was taken; identifying a defined braking capabilityof the host vehicle, a defined acceleration capability of the hostvehicle, and a longitudinal speed of the host vehicle; determining ahost vehicle braking distance based on an evaluation of: (i) the definedbraking capability of the host vehicle, (ii) the defined accelerationcapability of the host vehicle, and (iii) the longitudinal speed of thehost vehicle, wherein the defined braking capability of the host vehiclecomprises a minimum braking rate that is less than a maximum brakingrate of the host vehicle, wherein the minimum braking rate is identifiedto be applied by the host vehicle as at least an initial braking forceused to decelerate within the host vehicle braking distance, and whereinthe minimum braking rate is identified to be applied by the host vehicleas a lower limit of an amount of braking force used to deceleratethroughout the host vehicle braking distance; determining a targetvehicle braking distance, based on an evaluation of: (i) a longitudinalspeed of the target vehicle and (ii) a maximum braking capability of thetarget vehicle; and causing the host vehicle to implement the plannednavigational action when the predicted following distance of the plannednavigational action is greater than a minimum safe longitudinaldistance, wherein the minimum safe longitudinal distance is calculatedbased on the determined host vehicle braking distance and the determinedtarget vehicle braking distance.
 10. The machine-readable storage mediumof claim 9, wherein the minimum safe longitudinal distance includes anacceleration distance that corresponds to a distance the host vehiclecan travel over a time period at a maximum acceleration capability ofthe host vehicle, starting from the identified longitudinal speed of thehost vehicle.
 11. The machine-readable storage medium of claim 9,wherein the minimum safe longitudinal distance is further calculatedbased on a response time associated with the host vehicle.
 12. Themachine-readable storage medium of claim 9, wherein the defined brakingcapability of the host vehicle is based on weather and road conditionsof the environment.
 13. The machine-readable storage medium of claim 9,wherein the longitudinal speed of the target vehicle is determined fromthe sensing data.
 14. The machine-readable storage medium of claim 13,wherein the longitudinal speed of the target vehicle is determined fromoutput from at least one of a LIDAR system or a RADAR system of the hostvehicle.
 15. The machine-readable storage medium of claim 9, wherein theplanned navigational action causes at least one of steering, braking, oraccelerating in the host vehicle.
 16. The machine-readable storagemedium of claim 9, wherein the at least one sensor device includes acamera, and wherein the sensing data includes at least one imagecaptured from the camera.
 17. An apparatus, comprising: means forobtaining sensing data of an environment in a vicinity of a hostvehicle, the sensing data captured from at least one sensor device ofthe host vehicle; and at least one processing means for: determining aplanned navigational action for accomplishing a navigational goal of thehost vehicle; identifying, from the sensing data, a target vehicle inthe environment of the host vehicle; predicting a following distancebetween the host vehicle and the target vehicle that would result if theplanned navigational action was taken; identifying a defined brakingcapability of the host vehicle, a defined acceleration capability of thehost vehicle, and a longitudinal speed of the host vehicle; determininga host vehicle braking distance based on an evaluation of: (i) thedefined braking capability of the host vehicle, (ii) the definedacceleration capability of the host vehicle, and (iii) the longitudinalspeed of the host vehicle, wherein the defined braking capability of thehost vehicle comprises a minimum braking rate that is less than amaximum braking rate of the host vehicle, wherein the minimum brakingrate is identified to be applied by the host vehicle as at least aninitial braking force used to decelerate within the host vehicle brakingdistance, and wherein the minimum braking rate is identified to beapplied by the host vehicle as a lower limit of an amount of brakingforce used to decelerate throughout the host vehicle braking distance;determining a target vehicle braking distance, based on an evaluationof: (i) a longitudinal speed of the target vehicle and (ii) a maximumbraking capability of the target vehicle; and causing the host vehicleto implement the planned navigational action when the predictedfollowing distance of the planned navigational action is greater than aminimum safe longitudinal distance, wherein the minimum safelongitudinal distance is calculated based on the determined host vehiclebraking distance and the determined target vehicle braking distance. 18.The apparatus of claim 17, further comprising: sensing means forcapturing the sensing data.